Session LA: Turbulent Boundary Layers: Experimental Studies III

Observations of Large-Scale Meandering Motions in Rough-Wall Turbulence

Recent experimental evidence suggests the existence of meandering low-speed motions in the logarithmic region of smooth-wall turbulence with streamwise extents well exceeding the boundary- layer thickness. The present contribution explores the possible existence of these large-scale motions in turbulent flow over a rough surface. Time-resolved particle-image velocimetry experiments are performed in a streamwise--spanwise plane in the vicinity of a rough wall ($y\cong 0.065\delta$) replicated from a turbine blade damaged by deposition of foreign materials. This surface is highly irregular and contains a broad range of topographical scales. Taylor's hypothesis is utilized to reconstruct velocity fields over $8\delta$-long in the streamwise direction from the time- resolved PIV fields. Similar to previously-reported smooth-wall observations, these reconstructed velocity fields are marked by connected regions of low-speed fluid [$O(\delta)$ wide in the spanwise direction] that extend well beyond $\delta$ in the streamwise direction and meander significantly in the spanwise direction. In addition, wall- normal vortex cores of opposing rotation are found to populate the boundaries of these meandering, low-speed regions. The average characteristics of these motions in rough-wall turbulence are explored and compared to observations from smooth-wall flow.   

Addition of Isotropic Free-stream Turbulence Promotes Anisotropy in a Turbulent Boundary Layer

The effects of nearly isotropic free-stream turbulence in transitionally rough zero pressure gradient turbulent boundary layers are studied using data obtained from Laser Doppler Anemometry measurements. Measurements are carried out at Re$_{\theta }\le $ 11,300 with up to 6.2{\%} free-stream turbulence generated with an active grid. Remarkably, there is a large portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream results in significant increases in anisotropy of the turbulence. In order to quantify which turbulence length-scales contribute mostly to creating this trend, second order structure functions for velocity components u or v are examined at various distances to the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow.   

Inertial particle accelerations in a turbulent boundary layer

Two dimensional Lagrangian acceleration statistics of inertial particles in a turbulent boundary layer with free stream turbulence are determined by means of a high speed particle tracking technique (Ayyalasomayajula et al. PRL, 95, 144507, 2006). The boundary layer is formed above a flat plate, and water droplets are fed into the flow from sprays placed down-stream from an active grid, and from tubes fed into the boundary layer from humidifiers. The free stream Stokes number is varied from 0.035 to 0.47. As the boundary layer plate is approached, the tails of the pdfs narrow, become negatively skewed, and their peak occurs at negative accelerations (decelerations in the stream-wise direction). The mean deceleration and its r.m.s. increase to large values close to the plate and are more pronounced with increasing Stokes number, in marked contrast to what is found in isotropic turbulence where the acceleration r.m.s. decreases with increasing Stokes number. A model shows the significance of the combined effects of shear and gravity on the acceleration statistics. The work is funded by the US NSF.   

Complex dynamics of a boundary layer with free stream turbulence

Boundary layers in nature and in engineering applications often occur with turbulent free streams above them. Previous work by Hancock and Bradshaw (JFM, \textbf{205}, 1989), Thole and Bogard (J. Fluids Eng., \textbf{118}, 1996), and others has shown that free stream turbulence affects the statistics of a boundary layer significantly. In the present wind tunnel study using hot wire anemometry, a flat plate generates a boundary layer that is subjected to a variety of free stream turbulence conditions using active and passive grids. The free stream varies in turbulence intensity from 0.25{\%} to 11{\%} and in free stream turbulent Taylor- scale Reynolds number from 20 to 550. The ratio of the free stream length scale to the boundary layer thickness is also varied. Spectral data reveal a double-peaked energy spectrum, indicating the interaction of two different, major length scales. The double peak develops as the plate is approached from the free stream, and, though the feature is most pronounced at higher free stream Reynolds numbers, it is also evident at very low free stream turbulence intensities. This work was supported by the US NSF.   

High Aspect Ratio Cylindrical Boundary Flow and Wall Pressure Spectra

High resolution stereo-PIV measurements were made on a long ($>$ 1300 m), 38 mm diameter cylinder towed from a vertical strut at speeds of 7 to 30 kts. Wall pressure measurements were collected simultaneously at select axial locations. The experiments were performed in the high speed tow tank at NSWCCD. The cylinder was ballasted to be approximately neutrally buoyant and towed through a stationary laser sheet oriented perpendicular to the tow direction. The objective of the study was to quantify the boundary flow along the cylinder for correlation with the surface pressure data. The average velocity data was analyzed to compute boundary flow parameters used for nondimensionalizing the boundary layer pressure spectra. Mean and fluctuating streamwise and cross-stream velocities will be presented along with the corresponding pressure spectra.   

The Effect of Upstream Vane Wakes on Annular Diffuser Flows

Experiments were performed to determine the sensitivity to inlet conditions of the flow in two annular diffusers.~ One of the diffusers was a conservative design typical of a diffuser directly upstream of the combustor in a jet engine.~ The other had the same length and inlet shape as the first diffuser but a larger area ratio and was meant to operate on the verge of separation.~ Each diffuser was connected to two different inlets, one containing a fully-developed channel flow, the other containing wakes from a row of airfoils. Three-component velocity measurements were taken on the flow in each inlet/diffuser combination using Magnetic Resonance Velocimetry.~ Results will be presented on the 3D velocity fields in the two diffusers and the effect of the airfoil wakes on separation and secondary flows.   

Local flow topology dynamics in a turbulent boundary layer

Experimental data from time-resolved 3D Tomographic Particle Image Velocimetry is used to study the dynamics of the local flow topology in the logarithmic region of a turbulent boundary layer. Specifically, we determine the invariants of the velocity gradient tensor defining the local topology and compute their mean material derivatives as a function of the invariants themselves. Subsequent time integration yields trajectories, which reveal spiralling, periodic orbits representative of the flow evolution in the mean sense. The period is nearly constant and can be thought of as a characteristic life-time for the eddies. It has an associated wavelength of approximately 10~boundary layer thicknesses (using the local average velocity as the convective velocity). This corresponds well with the location where a peak appears in the pre-multiplied power spectra of the streamwise component of velocity in wall-bounded turbulence. Previous studies have linked that peak to the very large-scale motions or superstructures observed in wall turbulence. Hence, these results may provide a link between the local topology dynamics and the coherent structures commonly observed in boundary layers.   

Investigation of large-scale features in turbulent duct flows

Recent studies reveal that long low-speed meandering structures (referred to as ``superstructures'' or Very Large Scale Motions) exist in the log region of fully developed turbulent pipe and channel flows as well as the turbulent boundary layer. These studies have been carried out using hot-wire arrays which are physically limited in terms of wall proximity. Here we use an array of multiple wall skin friction sensors to study the ``footprint,'' that is, the influence of these large scale features at the wall. Hot-wire velocity profiles measured in conjunction with the multiple skin-friction sensor array are used to study the three dimensional coherence of the large scale structure and the ensemble averaged statistics. Experiments are carried out in fully developed turbulent pipe and channel flow facilities with a similar outer length scale (pipe radius, $R = 49.4{\rm mm}$ and channel half height, $h = 50{\rm mm}$) enabling direct comparison of the flows at a matched Reynolds number.   

Two-Point Cross-Spectral and POD Analysis of High Reynolds Number Zero Pressure Gradient Turbulent Boundary Layer

This study reports some of the two-point cross-spectral and proper orthogonal decomposition analyzes performed on the zero pressure gradient flat plate turbulent boundary layer experiments at R$_{\theta}=$9800 and 19,100. They are based on hot-wire measurements using a rake of 143 single wire probes placed in the LML wind tunnel, which has a 20 m long test section with approximately 30 cm of boundary layer thickness. Elongated correlations and their variation across the boundary layer are shown using two-point space-time correlations computed over very long records. The possible interaction between the inner and outer layer is discussed using the cross-correlations analysis and also a POD-based reconstruction of the velocity fields on a plane normal to the streamwise direction. Organization of the large scale structures on the same plane is also demonstrated using a combination of different spanwise Fourier and POD modes.   

Session LB: Turbulent Mixing II

Modeling the turbulent scalar fluxes in heated compressible flows

We use results from Direct Numerical Simulations of compressible flow in a heated channel (M{\_}cl = 0.34, 1.5) to advance an explicit, algebraic model for the turbulent scalar fluxes. The scalar fluxes of interest are the heat fluxes which enter into the equation for total energy and the mass fluxes which enter into the equations for turbulence kinetic energy and density variance. Both fluxes are usually modeled via gradient-transport hypothesis which does not account for the dependencies implied in the exact equations. Moreover, in fully-developed flows, the streamwise fluxes, which are greater than the fluxes in the direction of normal to the flow, are predicted as zero in models based on this hypothesis -- an outcome which is at variance with all results from experiments and simulations. The starting point is model is derived from the representation of the turbulent heat fluxes as a function of the Reynolds stresses, the mean strain rate and the mean vorticity. The time scales for the fluctuations in the scalar fields are often assumed to be proportional to the mechanical time scale. We test this assumption using the DNS results. The focus is on the near-wall region which determines the rate of heat transfer to the wall, and proposals for incorporation of a direct dependence of the heat fluxes on the gradients of mean density are examined.   

Performance of Turbulence Models in the Prediction of Heat Transfer from a Hemispherical Surface Due to Turbulent Jet Impingement

Impinging jet configurations are encountered in numerous industrial and engineering applications. Among these include cooling of a hot surface, turbine blade cooling, and airplane wing leading edge de-icing. In the design and operation of these applications, the knowledge of the heat transfer coefficient distribution along the cooling surface is important. We evaluated the performance of several turbulence models in the prediction of convective heat transfer due to round jet impingement onto convex spherical surfaces against available experimental data. The jet exit Reynolds number, the jet diameter, and the jet exit to the spherical surface distance were varied according to the experimental values. Based on calculated errors, the superiority of one model over the others cannot be established conclusively. However, the realizable k-epsilon model generally predicted the Nusselt number distribution more accurately than the other models for most cases.   

Mole fraction measurements in three species gas-phase turbulent flows

Planar imaging techniques are applied to measure the mole fractions of all major species in a nonreacting, acetone-helium jet issuing into air. Planar laser-induced fluorescence is used to measure the mole fraction of acetone, and planar Rayleigh scattering is used to measure the difference between the acetone and helium concentrations. Due to their differing molecular transport properties, and in particular disparate values of molecular diffusivity, the acetone and helium evolve differently and display different downstream concentration fields. Mole fraction profiles show a large-scale similarity between the concentrations of the two jet gases. The acetone field, due to the significantly lower diffusivity of acetone with air, has more small scale structure than the helium field. Scalar spectra for each jet species are presented, as well as the spectrum of the scalar difference, which represents the differential diffusion. Preliminary results suggest an anti-correlation to the scalars, particularly on the outside of the jet. For mixing simulations, this implies that there may be limitations to simulations that assume diffusivity can be represented with a single variable.   

Reynolds number dependence of thermal diffusion from a line source in decaying grid turbulence

Existing experiments on line source dispersion in isotropic turbulence are for low Reynolds numbers (Taylor scale Reynolds numbers of less than 100) and there has been no attempt to systematically vary the Reynolds number. Here we present new results of passive temperature fluctuations produced by a fine heated wire in decaying grid turbulence. The Taylor Reynolds number is varied from approximately 50 to 500 by means of active and passive grids. We study the dependence of the mean and r.m.s. temperature profiles on the Reynolds number. The effects of source size are also investigated. The results are compared with the recent modeling work of Viswanathan and Pope (Physics of Fluids, to be published) who find significant Reynolds number dependence but small effects when varying the source size. The peak centerline ratio of the r.m.s. to the mean of the scalar is also examined and compared with predictions. This work is funded by the US National Science Foundation.   

Experimental validation of a new closure scheme for turbulent diffusion using simultaneous PIV and PLIF

In this work the focus is on the moments of the probability density function (PDF) of scalar concentration, which normally can be inverted to approximate the PDF. To solve the moment equations of the PDF one requires a closure approximation for both the convective and dissipative terms. Sullivan (2004) proposed closures that provide a good qualitative representation of measured moment distributions across a plume from a line source in grid turbulence for the lowest four central moments. Simultaneous measurements of velocity and scalar concentration, using particle image velocimetry (PIV) and planer laser-induced fluorescence (PLIF) respectively, on a plume in a grid turbulence water tunnel experiment are used to quantitatively explore the closure scheme. The closures are validated by analyzing the velocity and concentration fields and considering an axisymmetric plume in cylindrical coordinates system.   

Optimization of pulsed jets in crossflow

Recent experiments (M'Closkey et al. 2002, Shapiro et al. 2006, Johari 2006, Eroglu \& Briedenthal 2001) on pulsed jets in crossflow show that jet penetration and spread can be optimized at specific pulse conditions. We performed DNS to study the evolution and mixing behavior of jets in crossflow with fully modulated square wave excitation. We attempt to explain the wide range of optimal pulsing conditions found in different experiments. Pulsing generates vortex rings. Sau and Mahesh (J. Fluid Mech., 2008) show that vortex rings in crossflow exhibit three distinct flow regimes depending on stroke ratio and velocity ratio. We use the behavior of a single vortex ring in crossflow to explain the evolution of pulsed jets in crossflow. Simulations suggest that the optimal conditions can be predicted from the transition between different regimes of vortex rings. It is observed that the duty cycle modifies the optimal conditions depending on the interaction in the near field. Simulation results and comparison with experiments will be discussed.   

Quantitative Measurement of Scalar Dissipation Rates in Turbulent Jets Using Planar Laser Imaging

Quantitative planar measurements in turbulent jet flows of scalar quantities, such as jet fluid mass fractions, $Y$, are relatively common, but planar measurements of the scalar dissipation rate, $\chi\propto\nabla Y\cdot\nabla Y$, are not. A complete understanding of the scalar dissipation rate field is important to applications such as turbulent non-premixed combustion. The particular challenge facing the measurement of $\chi$ is spatial resolution. Here, using planar Rayleigh scattering to measure $Y$ in helium-air and nonreacting acetylene-air jets, we measure $\chi$ from the near field up to $\approx 40$ jet diameters, $d$, from the jet exit using a series of five imaging windows. With this approach, the individual windows can be sized to ensure adequate pixel resolution to measure the local $\chi$, while the full set of data allows the measurement of the $\chi$ scaling over the entire axial range. Results indicate that the $\chi$ decay rates are slower than predicted from classical scaling arguments, and also slower than measured decay rates of kinetic energy dissipation. The data also permit assessment of the effects of spatial filtering on the measured $\chi$, which is relevant to efforts to model $\chi$ in combustion simulations.   

A dynamic subgrid-scale eddy diffusivity model with a global model coefficient for passive scalar transport in complex geometry

In the present study, a dynamic subgrid-scale eddy diffusivity model is proposed for large eddy simulation of passive scalar transport in complex geometry. The eddy viscosity model proposed by Vreman [Phys. Fluids, 16, 3670 (2004)], which guarantees theoretically zero SGS dissipation for various laminar shear flows, is utilized as the base eddy diffusivity model. The model coefficient is determined by the dynamic procedure based on the method proposed by Park {\it et al}. [Phys. Fluids, 18, 125109 (2006)] such that the model coefficient is globally constant in space but varies only in time. The large eddy simulations of passive scalar transport in turbulent channel flow and turbulent boundary layer are conducted and the proposed model shows nearly the same performance as the dynamic Smagorinsky model does. Since the proposed model does not require any {\it ad hoc} clipping and averaging over the homogeneous direction, it can be readily applied to transport of passive scalar in complex flows. Some other examples such as heat transfer in a ribbed channel will be shown in the final presentation.   

Large eddy simulations of turbulent coaxial jet flows with pulsation

Large eddy simulations of turbulent confined coaxial jet flows were performed at Re=9,000 based on the bulk velocity and outer radius of annular jet. Pulsations were superimposed on the inflow jets. The mean velocity ratio of annular jet to central jet is 1.667. The pulsation amplitudes of annular and central jets are 5{\%} and 20{\%}, respectively. Main control parameters were the pulsation frequency and the phase difference between annular and central jets. Effects of inflow pulsation on flow dynamics and mixing were investigated. We found that there exist two optimal pulsation frequencies: one is observed at St=0.327 for the minimum reattachment length on the chamber wall and the other is at St=0.180 for the maximum mixing in the shear layer. At the optimal pulsation frequency with the minimum reattachment length, effects of the phase difference between annular and central jets were scrutinized by examining the phase- or time-averaged turbulent statistics. The most effective phase difference for the reduction of reattachment length is obtained at 30$^{\circ}$, and for the maximum mixing enhancement is obtained at 270$^{\circ}$. For the phase difference 210$^{\circ}$, the reattachment length and mixing efficiency are almost the same as those of no-pulsation. Dynamics and interactions of vortical structures in the shear layers developed between two jet flows and between annular jet and chamber flow were studied. The mechanism of mixing enhancement was also discussed.   

Session LC: Turbulent Shear Layers and Mixing

Sensitivity Analysis of a Plane Mixing Layer using the Sensitivity Equation Method

Sensitivity field evolution of the incompressible, two-dimensional mixing layer to perturbations in both Reynolds number, $Re_{\delta_0}$, and Prandtl number, $Pr$, has been examined using the sensitivity equation method. In this method, the sensitivity coefficients (i.e., the partial derivative of vorticity and temperature with respect to $Re_{\delta_0}$ and $Pr$) are obtained from direct numerical simulation of the sensitivity equations coupled with the governing equations of the fluid motion. This is achieved using an unsteady finite volume based fractional step algorithm. Coherent structures in the sensitivity field depict mechanisms responsible for enhanced vortex growth and scalar mixing with increasing $Re_{\delta_0}$ and $Pr$, respectively. Two distinct configurations were found in the sensitivity field of vorticity. The first configuration represents an increasing growth in the mixing layer as $Re_{\delta_0}$ increases, while the second configuration depicts the saturation state for the vorticity field. The sensitivity of the temperature field to changes in $Pr$ exhibits a third configuration describing enhanced scalar with increasing $Pr$. These interpretations are confirmed with calculations of integral quantities, namely the rate of growth of the mixing layer with $Re_{\delta_0}$ and the evolution of the probability density function of the scalar field with $Pr$.   

Reduced Order Modeling for Beam Propagation through a Shear Layer

The performance of airborne platforms emitting or receiving light beams is severely hampered by the flow field around the turret mounted on the air vehicle. From a fluid dynamics point of view, the flow separating from the turret develops large, coherent structures. These structures are associated with density variations, which, from an optical point of view, result in large optical distortions. The goal of this research is to improve system performance by mitigating these structures using feedback flow control. While developing a feedback flow control system is a multi-step process, one important step is the design of a Reduced Order Model of the flow field under consideration. For the canonical flow field of a shear layer behind a backward facing step, both simulations results and experiments data are compared and used to provide input training data for the development of a neural network model based on Proper Orthogonal Decomposition of the flow field. The design of the neural network, based on the time coefficients obtained from Proper Orthogonal Decomposition, is shown and analyzed. The model of the flow field is then utilized to develop feedback control strategies to mitigate the optically detrimental coherent structures.   

Experimental Investigation of Optical Beam Propagation through a free Shear Layer

The performance of airborne platforms emitting or receiving light beams is severely hampered by the flow field around the turret mounted on the air vehicle. From a fluid dynamics point of view, the flow separating from the turret develops large, coherent structures. From an optical point of view, these structures due to their associated density variations, cause large optical distortions since the index of refraction is a function of density. The goal of this research is to reduce optical distortions by mitigating these structures using feedback flow control. For the canonical flow of a shear layer behind a backward facing step, both experimental measurements using hot film and Malley Probes and high resolution simulations are used to provide input data for model development. Based on the time coefficients obtained from Proper Orthogonal Decomposition of multiple open loop forced reference cases, the design of a global neural network based model of the flow field will be presented. A comparison between experiments, simulations and reduced order model will be presented.   

Fine-scale features in the far-field of a turbulent jet

The structure of a fully turbulent axisymmetric jet, at Reynolds number based on jet exit conditions of 5000, is investigated with cinematographic (1 kHz) stereoscopic PIV in a plane normal to the jet axis. Taylor's hypothesis is employed to calculate all three velocity gradients in the axial direction. The technique's resolution allows all terms of the velocity gradient tensor, hence strain rate tensor and kinetic energy dissipation, to be computed at each point within the plane. The data reveals that the vorticity field is dominated by high enstrophy tube-like structures. Conversely, the dissipation field appears to consist of sheet-like structures. Several criteria for isolating these strongly swirling vortical structures from the background turbulence were employed. One such technique involves isolating points in which the velocity gradient tensor has a real and a pair of complex conjugate eigenvectors. Once identified, the alignment of the various structures with relation to the vorticity vector and the real velocity gradient tensor eigenvector is investigated. The effect of the strain field on the geometry of the structures is also examined.   

Measurements in a High Reynolds Number Wake

Experiments were conducted in the Princeton/ONR HRTF windtunnel with highly pressurized air. The wake of a DARPA SUBOFF submarine model was measured over a large range of Reynolds numbers at 5 different downstream locations. The model is an axisymmetric body without appendages (fins) supported by a streamlined support, mimicking a semi-infinite sail. For all Reynolds numbers studied, the mean velocity distribution becomes self-similar between 3 and 6 diameters, $D$, downstream for the side where the support is not located. In contrast, self-similarity in the Reynolds stresses is not reached at the furthest downstream location ($x/D=15$). The spectra reveal two peaks in the near-wake. The lower wavenumber peak corresponds to a Strouhal number based on diameter and freestream velocity of about 0.22, suggesting that it is associated with an azimuthal or helical shedding mode in the wake. This mode is evident at all Reynolds numbers, at all cross-stream positions, indicating that it is unlikely to be due to the interference of the support wake with the model wake. The mode is seen only for $x/D<15$, suggesting that it plays a partial role in the approach to self-similarity of the turbulent stresses.   

Turbulent entrainment in jets: the role of the large and small scales of motion

This work analysis several large and small scale aspects of the turbulent entrainment mechanism that exists in mixing layers, wakes, and jets. The turbulent entrainment mechanism takes place across the turbulent/nonturbulent (T/NT) interface dividing the irrotational (nonturbulent - NT) from the turbulent (T) region in these flows. Recently da Silva and Pereira (Phys. Fluids, 20, 055101, 2008) using DNS of a turbulent plane jet analyzed the invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the T/NT interface in order to characterize the small scale dynamics near the T/NT interface. In the present work we focus on the intense vorticity structures (IVS) from the flow in order to analyze the interplay between the large and small scales of the flow during the turbulent entrainment. An interesting result is the existence of non negligible viscous dissipation rate outside the turbulent region. It turns out that this interesting phenomena is caused the the presence of IVS near the T/NT interface. The presentation will focus on how the presence of these IVS commands the evolution of many small scale quantities and ultimately imposes the entrainment rate.   

Three-Component Turbulence Measurement in Three Dimensional Wall jet

The lateral width of the turbulent 3-D wall jet is 5 to 8 times larger than the vertical height and is due to strong secondary flows. This makes the wall jet very difficult to model. The source of this streamwise vorticity is as yet unclear, although it has been linked to the anisotropy in the Reynolds stresses. The goal of this investigation is to simultaneously measure all three turbulent velocity components on and off the jet centerlines, so the sources of the streamwise vorticity can be determined. Here, the flow issues from a contoured nozzle with a diameter of 1.5 inches and a jet exit Reynolds number of around 2.5 X105. The three velocity components are measured with a four-wire-hot-wire probe in the far-field region.   

Experimental Model of Contaminant Transport by a Moving Wake Inside an Aircraft Cabin

The air cabin environment in jetliners is designed to provide comfortable and healthy conditions for passengers. The air ventilation system produces a recirculating pattern designed to minimize secondary flow between seat rows. However, disturbances are frequently introduced by individuals walking along the aisle and may significantly modify air distribution and quality. Spreading of infectious aerosols or biochemical agents presents potential health hazards. A fundamental study has been undertaken to understand the unsteady transport phenomena, to validate numerical simulations and to improve air monitoring systems. A finite moving body is modeled experimentally in a 10:1 scale simplified aircraft cabin equipped with ventilation, at a Reynolds number (based on body height) of the order of 10,000. Measurements of the ventilation and wake velocity fields are obtained using PIV and PLIF. Results indicate that the evolution of the typical downwash behind the body is profoundly perturbed by the ventilation flow. Furthermore, the interaction between wake and ventilation flow significantly alters scalar contaminant migration.   

Dependence of higher-order passive-scalar structure functions on the scalar-field initial conditions

To investigate the dependence of structure function scaling exponents of a turbulent passive scalar on the (scalar-field) initial conditions, higher-order structure functions of temperature are measured in the turbulent wake of a circular cylinder ($R_\lambda = 388$). The turbulent scalar field is generated by two different means. It is first created by heating the cylinder. It is then produced using a mandoline.\footnote{Warhaft and Lumley, 1978, {\it J. Fluid Mech.}, {\bf 88}, 659-684.} Though the second-order statistics ({\it e.g.}, power spectra, second-order structure functions) of the scalar field are experimentally indistinguishable (in the inertial and dissipative ranges) for the two cases, we observe notable differences in the inertial-range scaling exponents ($\zeta_n$) of the n$^{th}$-order passive-scalar structure functions at higher orders ($n \geq 4$). The implication is that the variations in previous estimates of $\zeta_n$ observed in different experiments may be i) attributable to differences in the scalar field initial conditions, and therefore ii) inconsistent with a universal nature of the small-scale statistics of a passive-scalar field.   

Mixing Characteristics of Strongly-Forced Jet Flames in Crossflow

The effects of high frequency, large-amplitude forcing on the characteristics of a non-premixed jet flame in crossflow (JFICF) at mean Reynolds numbers of 3,200 and 4,850 are studied experimentally. Harmonic forcing of the jet fuel results in a drastic decrease in flame length and complete suppression of soot luminosity. Visualization by planar laser Mie scattering shows that forced JFICF, similar to forced free or coflow jet flames, are characterized by ejection of high-momentum, deeply penetrating vortical structures. These structures rapidly breakdown and promote intense turbulent mixing in the near region of the jet. The rapid mixing resembles a ``one-step'' process going from a fuel rich state far in the nozzle to a well-mixed, but significantly diluted, state just a few diameters from the jet exit plane. Exhaust gas emissions measurements indicate a decrease in NOx, but increases in CO and unburned hydrocarbons with increasing forcing amplitude. Acetone PLIF measurements are used to investigate the effect of partial-premixing on these emissions findings.   

Session LD: Richtmeyer-Meshkov Instabilities

Experimental analysis of re-shocked gas curtain

Results are presented from experiments studying the interaction of a planar shock wave of strength $M \sim $1.2 with a thin fluid layer of SF$_{6}$ gas imbedded in air. Flow visualizations are obtained using planar laser diagnostics (simultaneous PLIF/PIV measurements) rather than integral measures. A concurrent study at the lab has shown that the interaction of first shock wave with the thin fluid layer does not lead to a fully-developed turbulence stage, during the investigation window, for low-Mach number experiments. Therefore, this study is primarily focused on the turbulent mixing induced by the reshock of an already shocked interface. As the shock wave reflected from the end-wall of the test section passes through the already evolving SF$_{6}$ layer, the intense vortical and nonlinear acoustic phenomenon are observed, including dramatic changes in the length scales and topology of the evolving mushroom structures, intense mixing, and finally transition to the fully-turbulent stage characterized by fine scales in the flow field. The location of end-wall is changed during the experiments to achieve reshock of the interface at different times (different initial conditions).   

Memory of Initial Conditions in Shocked and Re-shocked Heavy-Gas Curtains

We experimentally investigate the memory of initial conditions in the concentration fields of Richtmyer-Meshkov-unstable flows. We consider shocked heavy-gas curtains in air for several initial conditions at Ma = 1.2. The concentration of the heavy gas is measured using planar laser-induced fluorescence, and spanwise power spectra of the concentration fields are computed from the PLIF data. The periodic initial conditions leave a clear imprint in the spectra as forcing modes, and the evolution of these modes is tracked over time. The effects of a stronger initial shock (Ma = 1.5), a second incident shock, and variations in the initial conditions on the persistence of the forcing modes in the spectra are investigated.   

Turbulence Statistics in a Richtmyer-Meshkov Unstable Thin Fluid Layer after Reshock

We present true ensemble-averaged turbulence measurements of the density, velocity and density-velocity cross-statistics in a Richtmyer-Meshkov unstable varicose fluid layer after reshock. The instantaneous fields that comprise the ensemble at various times are obtained using high resolution simultaneous PIV-PLIF diagnostics employed on a repeatable fluid layer subjected to a Mach 1.2 shock and a subsequent reflected reshock. Sufficiently after reshock, the profiles of the density self-correlation show a double-peak structure, with the location of the peaks coinciding with the edges of the turbulent structure. The RMS of the fluctuating streamwise and spanwise velocities across the layer are observed to carry similar magnitudes pointing to a tendency of the flow to attain homogeneity. For the first time, experimentally measured density-velocity correlations will be presented to complete all the components of the 2D Reynolds stress tensor. Errors associated with the light propagation through the inhomogeneous turbulent medium, and the effects of different averaging procedures used in the calculation of the turbulence statistics will be evaluated to provide tight bounds on the present measurements. Finally, the connections of the various measurements to terms in the equations for the mass flux, kinetic energy and density self-correlation will be exemplified.   

Simulations of a Reshocked Varicose Gas Curtain

The evolution of a varicose curtain of SF$_{6}$ gas accelerated by a Mach 1.2 shock wave in air and then reshocked 600 $\mu $s later has been examined both experimentally and computationally. Two-dimensional simulations incorporating the experimental initial conditions have been performed using RAGE, an adaptive-mesh Eulerian code. The effects on the flow before and after reshock are examined and the results are compared with experimental images of the curtain's evolution. Also a sub-grid mix model in RAGE is applied to the simulations and the computed density and velocity correlations are compared with data available from the experiment.   

Hybrid WENO/Central Difference Navier-Stokes Simulation of Reshocked Richtmyer-Meshkov Instability

A new hybrid WENO/central finite-difference method has been developed for the high-resolution, multi-dimensional, efficient simulation of turbulent mixing induced by interfacial hydrodynamic instabilities. Multi-resolution analysis is used to dynamically determine regions in which large gradients or discontinuities exist (where upwinding is applied) and regions in which the flow is smooth (where central differencing is applied). This method is used to solve the dissipative fluid dynamics equations describing reshocked Richtmyer--Meshkov unstable flow in the Mach $1.3$ Jacobs--Krivets and Mach $1.5$ Vetter--Sturtevant shock tube experiments. The mixing layer widths are shown to be in good agreement with experimental data on the growth of the layer. Additional quantities not measured in the experiment, such as local and global molecular mixing parameters, energy spectra, and statistics are also calculated and compared (when possible) to previously obtained results using monotone-integrated large- eddy simulation and implicit large-eddy simulation methods.   

Richtmyer-Meshkov Instabilities with Shocks, Reshocks, and Rarefactions

We point out a variety of experiments that can be carried out at a National Shock Tube Facility to study Richtmyer-Meshkov instabilities generated by reshocks and rarefactions. The rarefactions may be isolated, preceded by a shock, or followed by a shock. Numerical simulations with CALE will be presented and compared with a generalization of the nonlinear Layzer model that includes time-dependent densities.   

Richtmyer-Meshkov Experiments on a Reshocked, Low Atwood Number Interface

Low Atwood number (A = ($\rho _{2}$--$\rho _{1})$/($\rho _{2}+\rho _{1})$ = 0.29) Richtmyer-Meshkov instability (RMI) experiments are presented for a near single mode, sinusoidal interface accelerated by an incident and a reflected shock wave. The interface is created by flowing a 50-50{\%} mixture of He+Ar from above and pure Ar from below. Slots at the interface location allow for a stagnation plane to form. A pair of pistons embedded in the shock tube walls force a near sinusoidal, linear ($\eta $/$\lambda $ = 0.01), standing wave, which is accelerated by a $M$ = 1.3 planar shock wave. The setup at the Wisconsin Shock Tube Laboratory allows for the interface development to be observed for a long period ($\sim $8 ms) after the interface is reshocked by the shock wave reflecting off the end wall and before the expansion wave reflected from the driver section end wall reaches the interface. The interface is visualized with planar Mie scattering. The additional vorticity deposited on the interface during reshock causes the spike and bubble to invert phase and grow at a substantially higher rate than before reshock. The experimental results are compared to numerical simulations using the Eulerian AMR code \textit{Raptor} (LLNL).   

Experimental investigation of a twice-shocked spherical gas inhomogeneity

Results are presented from a series of experiments and simulations studying the behavior of a spherical gas inhomogeneity impulsively accelerated by an incident and a reflected shock wave. Two Atwood numbers are studied using soap film to create argon and sulfur-hexafluoride bubbles impacted by a planar shock wave of strength $M $= 1.33. The experiments are performed in a 9.2-m-long vertical shock tube with a square internal cross-section, 25.4 cm per side. The bubbles are released from an injector that is pneumatically retracted into the side of the shock tube. For the scenario involving an Argon bubble free falling in ambient nitrogen (A = 0.176), the reshock occurs during the tail end of the bubble's compression regime after it has already shown slight growth and vortex core development. For the SF6 bubble free falling in ambient nitrogen (A = 0.681), the reshock occurs later in the bubble's developmental stage. The flow is visualized with planar Mie scattering and temporal evolutions are analyzed for the spatial dimensions, growth rates and vorticity estimates. PIV analysis is performed for several instances using the soap film as tracer particles. These trends are compared to simulations performed with the Eulerian AMR hydrodynamics code \textit{Raptor }from LLNL.   

Interaction between gas cylinder seeded with droplets and an oblique shock

The problem of a planar shock interaction with gas curtains (cylinders) whose plane (axis) of symmetry is parallel to the plane of the shock has been well studied both experimentally and numerically, and in this case, the flow evolution driven by Richtmyer-Meshkov instability is well characterized. However, for a similar \emph{oblique} interaction, with the plane of the shock and the plane (axis) of the density interface being non-parallel, presently only numerical results exist. This problem, however, would be quite interesting to study experimentally both because of a variety of relevant applications and because oblique shock interaction adds large-scale three-dimensionality to the initial conditions. Here we report on the progress of our work on the development of a tiltable Mach 3 shock tube designed specifically to produce such oblique shock interactions and equipped with diagnostics suitable for studies of three-phase flow (light gas, heavy gas, and particles/droplets). The presence of the droplets (or particles) introduces several additional interesting issues here, including the possible effect of shock focusing on the non-gaseous phase carried by the flow.   

A detailed numerical investigation of the single-mode Richtmyer-Meshkov instability

The single-mode shock-driven Richtmyer-Meshkov (RM) instability is investigated using high resolution numerical simulations.\footnote{Numerical study of the single-mode Richtmyer-Meshkov instability for a comprehensive set of conditions, A. Dhotre, P. Ramaprabhu \& Guy Dimonte, To be submitted to Physics of Fluids.} The growth rate of an initially sinusoidal perturbation is evaluated against linear theory and an impulsive model over a wide range of influential parameters: [A, Ma, 2D/3D, $\gamma$$_{1}/$\gamma$$_{2}$, ka$_{0}$]. The results are in good agreement with linear theory for small amplitudes, and with the impulsive model when compressibility effects may be ignored. For large density differences, spikes exhibit acceleration above the velocity predicted by linear theory, while bubbles decay from the start. The spike acceleration disappears with larger initial amplitudes consistent with simple potential-flow models.\footnote{Modeling of the single-mode Richtmyer-Meshkov instability for a comprehensive set of conditions, Guy Dimonte, P. Ramaprabhu \& A. Velikovich, To be submitted to Physics of Fluids.} Our results present a consistent but complicated picture of the early-stage growth of both small and large amplitude RM, and clarify the regimes of validity in parameter space of several existing linear and nonlinear theories.   

Session LE: Control of Instabilities

A realistic model of a wall-transpiration actuator for boundary layer control

Experimental studies of boundary layer control using continuously distributed wall-suction usually implement suction by applying a pressure gradient to a layer of porous material via an underlying plenum chamber. Theoretical studies, however, usually neglect the penetration of fluid into the porous layer and plenum chamber by forcing the base flow and velocity perturbations to vanish at the interface with the porous layer. We present a realistic model of a wall-transpiration actuator which implements suction through a fluid saturated, rigid, homogeneous, isotropic, porous layer stretched over a semi-infinite plenum chamber. We test our model on the asymptotic suction boundary layer (ASBL) and perform a linear stability analysis. We take account of the full coupling between the flow fields in the boundary layer, porous layer, and plenum chamber using boundary conditions derived by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer, Vol. 38, 1995, pp 2635-2646). We illustrate the impact of wall-permeability, porous layer thickness, and the plenum chamber on the critical Reynolds number and the stability of the Tollmien-Schlichting wave. We use our model to find the optimal operating conditions of an ASBL which minimize the skin friction drag and power required to apply the suction.   

Global mode analysis of the stabilization of bluff-body wakes by base bleed

Base bleed is a simple and well-known means of stabilizing the wake behind slender bodies with a blunt trailing edge. In the present research, we investigate the global instability properties of the laminar-incompressible flow using a spectral domain decomposition method to perform the global stability analysis. In particular, we describe the flow instability characteristics as a function of the Reynolds number, Re=$\rho W_{\infty}D/\mu$, and the bleed coefficient, defined as the bleed-to-freestream velocity ratio, $C_b=W_b/W_{\infty}$, where $D$ is the diameter of the body, $\rho$ and $\mu$ the density and viscosity of the free stream, respectively. A first stationary bifurcation for, Re $\simeq$ 364, is found, and a second oscillatory bifurcation for, Re $\simeq$ 598, with a Strouhal number, St= 0.105, both for the most unstable azimuthal mode $|m|$= 1. We also report the existence of a critical bleed coefficient to stabilize both the first, $C^*_{b1}=C^*_{b1}(Re)$, and the second, $C^*_{b2}=\, C^*_{b2}(Re)$, bifurcations such as $C^*_{b1}>C^*_{b2}$ for the range of Reynolds number under study, $0 \leq Re \leq 2000$. For $Re > \,600$ the same kind of bifurcations are found for the azimuthal modes $|m|$= 2 and $|m|$= 3, which exhibit similar behaviors as the $|m|$= 1 mode with respect to the critical bleed coefficient.   

Flow control by combining radial pulsation and rotation of a cylinder in uniform flow

Flow visualizations and hot-wire measurements are carried out to study a circular cylinder undergoing simultaneous radial pulsation and rotation and placed in a uniform flow. The Reynolds number is in the range of 1,000--22,000, for which transition in the shear layers and near wake is expected. Our previous experimental and numerical investigations in this subcritical flow regime have established the existence of an important energy transfer mechanism from the mean flow to the fluctuations. Radial pulsations cause and enhance that energy transfer. Certain values of the amplitude and frequency of the pulsations lead to negative drag (i.e.\ thrust). The nonlinear interaction between the Magnus effect induced by the steady rotation of the cylinder and the near-wake modulated by the bluff body's pulsation leads to alteration of the omnipresent K\'{a}rm\'{a}n vortices and the possibility of optimizing the lift-to-drag ratio as well as the rates of heat and mass transfer. Other useful applications include the ability to enhance or suppress the turbulence intensity, and to avoid the potentially destructive lock-in phenomenon in the wake of bridges, electric cables and other structures.   

Harmonically forced enclosed swirling flow

The response of steady state flows in a cylinder driven by a harmonically modulated rotating endwall is investigated experimentally and numerically. Three dynamic regimes are identified. For very low forcing frequency, the synchronous flow approaches quasi-static adjustment, and for very large forcing frequencies the oscillations are localized in the boundary layers on the cylinder. These localized wall oscillations drive the synchronous flow in the interior to the underlying axisymmetric steady basic state. The third regime occurs for forcing frequencies in the range of the most dangerous axisymmetric Hopf eigenfrequencies, with the 1:1 resonances leading to greatly enhanced oscillation amplitudes localized in the axis region where the flow manifests vortex breakdown recirculation zones. By comparing the spatio-temporal structure of the junction vortices produced by the modulations in this range of frequencies with the vorticity eigenfunctions responsible for the self-sustained oscillations in the unmodulated problem, we have identified the mechanism responsible for the large amplitude pulsations of the vortex breakdown recirculations on the axis at mean rotation rates well below critical for the self-sustained vortex breakdown oscillations. An important consequence of this study is that to achieve a strong resonant effect, it is not sufficient to only consider the temporal characteristics of the flow state, but that the imposed forcing must also match the spatial characteristics.   

System identification and model-based control of two-dimensional cavity oscillations

Direct numerical simulations are used to characterize the resonant instabilities in two-dimensional compressible flow over a rectangular cavity. Specifically, by first using a dynamic phasor model to stabilize the flow, the cavity's linear open-loop transfer function is determined. The transfer function's input and output consist of a body force at the cavity leading edge and a pressure measurement on the trailing edge wall respectively. The transfer function found allows comparison with and validation of a linear model of the cavity. The empirical transfer function is also used to design a model-based feedback controller, useful for reducing oscillations at a a single operating point, or as a starting point for an adaptive controller. Numerical simulations of the closed-loop system show that the model-based controller successfully stabilizes the cavity flow.   

Adjoint Analysis of a Compressible Channel Flow

We present an adjoint analysis of a compressible channel flow using Direct Numerical Simulation. The final aim of this study is to build a tool to perform control of the aerodynamic noise. The adjoint equations are derived from the 2D unsteady compressible Navier-Stokes equations, and are computed backward in time. Both systems are discretized using a 6th order compact scheme in space and 4th order Runge-Kutta scheme in time. Appropriate wall boundary conditions are derived and validated for the adjoint system. We perform sensitivity analysis by applying different kinds of forcing to the adjoint equations, where the resulting field shows the forcing of the direct system required to obtain a given effect. In this study, we are interested in finding which perturbation creates higher noise levels at the core flow (i.e. in a position far from the wall) and how to reduce it. This test case is the first step to perform adjoint analysis of more complex wall-bounded flows, and to perform optimal open-loop control to reduce noise.   

Reduced-Order Estimator-Based Feedback Control of Transitional Channel Flow

Reduced-order models obtained using empirical balanced truncation and balanced proper orthogonal decomposition (BPOD) are used for feedback control of transitional channel flow. The models are developed for linearized flow and the controllers designed for the models are then applied to full DNS simulations. Both localized body forces and wall blowing/suction are used as actuation. Low-order computationally efficient estimators based on the models are designed for all cases, and the state estimates are computed from measurements of wall shear or velocity inside the channel. As a measure of controller performance, we demonstrate that transition energy thresholds for the nonlinear evolution of certain classes of standard perturbations, including localized perturbations and optimals at different wavenumbers, are successfully increased by applying our feedback controllers.   

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

We present a computational algorithm for model reduction of high-dimensional fluid simulations based on the Eigensystem Realization Algorithm (ERA), a method often used for system identification of vibrating systems. Our goal is to obtain models that capture the underlying flow physics and, at the same time, are useful for control design. For that purpose, we consider a system whose output is the velocity field in the entire computational domain. For such a large number outputs, ERA is intractable, so we use a technique called output projection, which involves reducing the number of outputs by projecting them onto the most energetic POD modes of the impulse response of the system. The presented algorithm involves a simple snapshot-based procedure commonly used for POD or balanced POD. The resulting models are equivalent to those obtained using balanced POD, but the algorithm involved requires only $O(n)$ inner products as compared to $O(n^2)$ for balanced POD, and does not need any adjoint simulations as required for balanced POD, thus resulting in large computational savings. We apply this technique to 2D flows past a flat plate at a low Reynolds number, and obtain reduced order models of the flow linearized about stable and unstable steady states.   

Modelling for Feedback Control of Skin Friction Drag in Algebraic Growth

We address the following problem: given spanwise arrays of wall- mounted shear-stress sensors at upstream and downstream locations, obtain accurate estimates of the flow field above an array of actuators located between the sensors. The accuracy of these estimates is of crucial importance in the design of any closed-loop drag reduction controller. To achieve satisfactory estimates we employ feedback from the sensors in conjunction with a dynamic model, based on that of Luchini (2000), describing perturbation evolution within a laminar boundary layer. The novelty of this work lies in the derivation of a state-space model of sufficiently low order to enable Kalman filter synthesis. Rather than obtaining a reduced- order model via numerical methods such as balanced truncation (Zhou, Doyle, Glover; 1996), we employ a series of approximations based on the results of Andersson, Berggren et al. (1999), to derive a low-order model analytically. A Kalman filter is synthesised and tested on the algebraic growth region of the DNS of Zaki (2005). Despite the use of a low-order model and significant free-stream turbulence, the results demonstrate good performance of the filter.   

Session LF: Jet and Cavity Flows

Investigation of the Near-Field Acoustic Properties of Imperfectly Expanded Supersonic Jets using Large-Eddy Simulations

Numerical simulations of Imperfectly Expanded Supersonic Jets from a CD nozzle representative of those used in military engines have been carried out. A MILES (Monotonically Integrated Large Eddy Simulations) approach with a finite element version of Flux-Corrected Transport algorithm (FEM-FCT) is used. FEM-FCT is able to accurately implement nozzle geometries and is ideal for simulating shock-containing flows. We have simulated a wide range of under-and over-expanded flow conditions as well as the design condition. The distributions of the centerline static pressure and noise spectra are in good agreement with the corresponding experimental data. It is found that this type of nozzle is not shock free even at the design condition due to the sharp change of the geometry in the throat area. The near-field acoustics is investigated, and screech tones are observed in all cases except in an over-expanded case with a low total pressure ratio. The frequencies of the screech tones are in good agreement with both the theoretical prediction and the measurement. The noise source locations are investigated by studying the noise distributions at peak frequencies and the correlations between pressure and other flow quantities.   

Nonlinear Parabolized Stability Equation Models for Turbulent Jets and their Radiated Sound

We investigate the nonlinear and non-parallel stability characteristics of round jets using the Nonlinear Parabolized Stability Equations (NPSE) supplemented with a turbulence model. We adopt an approach where both the meanflow and Reynolds-averaged stresses from a RANS simulation serve as input to the NPSE. We compare our predictions to measurements in the both the near and far fields of a turbulent round jet. We also compare our methodology to previous NPSE calculations for planar mixing layers and jets.   

Investigation of the Near-Field Acoustic and Flow Properties of Imperfectly Expanded Supersonic Jets using Particle Image Velocimetry

The flow fields of imperfectly Expanded Supersonic Jets from conical CD nozzles are investigated by Particle Image Velocimetry. This nozzle geometry represents the exhaust nozzles on high-performance military engines. The results are compared with shadowgraph to bring out the details of the highly accelerated regions where seed particles may lag behind the flow, viz. the shocks and Prandtl-Meyer fans. Nozzles with three area ratios are examined over a wide range of under- and over-expanded conditions as well as the design conditions for each nozzle. It is found that this type of nozzle is not shock free at the design condition due to the sharp change of the geometry in the throat area. Both near-field and far-field acoustic measurements are presented. Flow-field and near-field acoustic measurements are compared with Numerical simulations in the accompanying presentation by Liu, Kailasanath and Ramamurti. The distributions of the centerline static pressure and noise spectra are in good agreement with the corresponding experimental data.   

Propagation of Ultrasound Waves inside a Supersonic Jet

We use a Rayleigh scattering technique to detect density fluctuations in a supersonic air jet. The technique gives the spatial Fourier transform of the density fluctuations for a wave vector given by the experimental set-up. The method works as a nonintrusive microphone that can measure inside the flow. We measure at different locations inside and outside the flow to determine the emission pattern. We can determine the propagation inside the flow, the diffraction through the mixing layer and the propagation outside the jet.   

An Asymptotic Description of Supersonic Jet Modes

We present a large-axial-wavenumber asymptotic analysis of inviscid normal modes in supersonic jets. A complete map of inviscid instabilities is obtained for different perturbation azimuthal wavenumbers. We demonstrate the existence of four kinds of modes according to their convective Mach number, defined as the ratio of their phase velocity by the speed of sound: counterflow subsonic waves, subsonic waves, radiating waves (supersonic waves) and Kelvin-Helmholtz instabilities. We provide the general conditions for each kind of this modes to exist, and by means of WKBJ analysis, the dispersion relation and an explanation for the physical mechanism of instability. Finally, we explore the limit of large Mach numbers (hypersonic flows), in which the dominant unstable modes are the radiating waves.   

Performance Results for the Optical Turbulence Reduction Cavity

The testing of a new optical turbulence reduction cavity model from Mach 0.3 to 1.5 in the Trisonic Gasdynamics Facility (TGF) has occurred. The current model has optical quality fused silica windows that will allow non-intrusive flow field measure to be made. The results presented will compare the current optical turbulence reduction cavity model with the historic data from the old turbulence reduction cavity model that was built in the mid 1970s. Various flow control techniques to reduce the sound pressure level and overal sound pressure level inside the cavity were also exmanied and thier preformance results will be shown.   

Development and Calibration of a Reduced Order Modelling for subsonic cavity flows

In this study we propose a new calibration technique for the development of a Reduced Order Model (ROM) for a compressible cavity. A DNS is performed for a 2D rectangular cavity at a Mach number of 0.6 and a Reynolds number of 52 (based on the mometum thickness) which corresponds to a shear mode of the cavity oscillations. The technique of Proper Orthogonal Decomposition (POD) is utilised to get the most dominant flow dynamics, a ROM based on the isentropic equations is developped by projecting the governing equations on the subspace spanned by the POD modes resulting in a dynamical system. The dynamical system is then utilised to predict the flow dynamics, but the main disadvantage of the ROM is that the system fails to predict the large time temporal dynamics. In this work we propose a way to stabilise the dynamical system to predict accurately the flow dynamics. This enhances the usefulness of the ROM for control applications.   

Effect of Cavity Width on the Self-sustained Oscillation in a Low-Mach-number Cavity Flow

Recent unsteady-wall-pressure and velocity measurements (Zhang and Naguib, AIAA paper 4376-2008) in finite-width and azimuthally-uniform cavities showed that a low-Mach-number ($M <$ 0.1) cavity has distinct behavior with different width-to-length ($W/L)$ ratios and a turbulent boundary layer at separation. The cavity was defined as a \textit{narrow cavity} if $W/L<$1 and a \textit{wide cavity} if $W/L>$1. In the latter case, the self-sustained oscillation was attenuated \textit{and}, instead, low-frequency disturbances became dominant. This effect was more pronounced with increasing Reynolds number. This interesting finding is believed to relate to the recently uncovered three-dimensional instability of the cavity and its interaction with the shear layer (Bres and Colonius \textit{JFM} \textbf{599}, 2008). To explore this idea further, the distribution of the unsteady wall pressure along the azimuthal direction and the flow velocity are measured simultaneously. The results give better understanding of the nature of the low-frequency unsteadiness, the three dimensionality of the flow in the cavity and the effect of cavity width on them.   

Session LG: Drops VI

Numerical Studies of the Aspiration of Small Drops Using a Micropipette

Aspiration of small drops, vesicles, or biological cells using a micropipette has been used as a means of characterizing the properties of the interface or membrane. The basic idea is that the shape of the deformable particle can be imaged, and this data can be translated into information about the interface or membrane properties by comparison with theoretical predictions. For the simple case of a drop, there is a critical condition of flow rate or pressure drop that depends on the interfacial tension (among other parameters) beyond which the drop is aspirated completely into the pipette. With a proper theory, this critical condition can then be used to determine the interfacial tension. Experiments to date when interpreted using a static force balance (neglecting all viscous forces) yield literature values for the interfacial tension. In this study, we use axisymmetric boundary integral methods for drops of different sizes relative to the pipette and different viscosities relative to the suspending fluid, in order to establish the range of validity of this simple method of data interpretation.   

Micron-scale droplet deposition from a retreating syringe

Contact drop dispensing is initiated by the formation of a liquid bridge between the substrate and a dispensing syringe. As the syringe retreats, the liquid bridge stretches grows and breaks, leaving a drop on the substrate. The dynamics of liquid bridge breaking have broad interests in crystal growth, inkjet printing and micromanipulation, and contact drop dispensing has many applications in manufacturing and process control. The dynamics of the drop formation are surprisingly complex and the resulting droplet size can vary by orders of magnitude depending on the syringe diameter, $d$, fluid properties and syringe retraction speed, $u$. Experiments show that at low retraction speeds, arbitrarily large drops can be formed, their size scaling with $u^{-1/2}$. At a critical speed, the contact line on the substrate reverses direction and shrinks rather than expands as the needle retreats. Above this speed, droplets as small as 50 microns can be formed - much smaller than the characteristic needle dimension ($d\approx 500\mu$m). The limiting droplet size appears to be determined by dynamics of the contact line. We present experimental results and scaling based on measurements over a wide range of physical and geometric parameters.   

The role of Peclet number in 3-D mixing inside drops

We consider the problem of mass transfer from a circulating liquid drop in which the flow produces 3-D chaotic trajectories of passive non-diffusing particles. The aim is to investigate effect of Peclet number, Pe, on the transport rates in such situations. The flow field is produced by applying an axial electric field, and by switching the field direction through an angle $\beta$ at constant time intervals. The 3-D advection-diffusion equation is solved numerically to obtain the concentration field, and the total mass in the drop follows an exponential decay. The enhancement factor, defined as the decay constant normalized by that for diffusion alone, shows a steep increase with Pe for large Pe, indicating large enhancement of the transport rate. An optimal switching period that maximizes the enhancement is obtained. Movies of the simulations shows the existence of periodically repeating spacial structures in the concentration field (``strange eigenmodes'').   

Electrospray Droplet Structures Imaged Using Digital Holographic PIV

We present holographic measurements of an electrospray, illustrating the three-dimensional spatial structure of droplets after jet breakup including droplet divergence.~A conducting fluid (doped isopropanol) subjected to strong electric fields on the order of 300 kV m$^{-1}$ forms a Taylor cone, which emits a jet from the cone apex (tip streaming). Surface tension forces neck the jet into 2 $\mu $m diameter droplets, which subsequently diverge into a complex spray due to an instability involving Coulombic repulsion forces between the like-charged droplets. We use digital in-line holography with dual, pulsed Nd:YAG lasers to illuminate the droplet spray near the divergence region. Droplets are detected by reconstructing the three-dimensional intensity field from the recorded holograms. Due to the high-speed of the droplets (approximately 100 m/s), a unique imaging system is employed, which is described in the presentation.   

Effect of AC and DC electric fields on the residence time of coalescing drops

The residence time of de-ionized water droplets undergoing coalescence at a planar silicon oil/water interface under AC and DC electric fields is investigated with the aid of high-speed digital photography. We show that the residence time is composed of two sequential stages, which are dominated by deformation and drainage, respectively. Previously developed models predict that residence time occurs in a single stage that is dependent singularly on the magnitude of the electric field; our experiments, however, show that the frequency is also important. In the first stage, the underside of the droplet begins to deform as soon as the electric field in the gap between the droplet and fluid bulk reaches a critical value; although this value is constant for any set of experimental parameters, the first stage residence time should be frequency dependent, as is shown in our experiments. In the second stage, the residence time is dependent only on the drainage of the interfacial fluid film, and thus is inversely proportional to the strength of the electric field and independent of frequency; our results for the second stage are in good agreement with the previously developed model.   

Stability determination of crude oil emulsions by electrorheological measurement

Emulsion stability is paramount to the success of many industrial applications and the remediation of naturally undesirable occurring fluid-fluid dispersions. Bottle tests and critical electric field (E$_{c})$ measurements are two commonly used techniques to interpret emulsion stability. In the former, the amount of water resolved after gravitational settling test or centrifugation as a function of time is used as an indicator of stability. Generally, the lower the total water fraction resolved, the higher the emulsion stability. In the second method, the value of E$_{c}$ leading to drop coalescence is used as an indicator of stability. A larger value of E$_{c}$ is a reflection of a more stable dispersion. The value of E$_{c}$ is usually determined by measuring a sudden increase in electrical conductivity in water-crude oil emulsions as the field value is increased. In this work, an electrorheological test is used to establish the value of E$_{c}$ and hence the stability criterion. Results of electrorheological measurements are compared to results of bottle tests for water-crude oil emulsions with or without stabilizing solid micro-particles. Results will show the consistency among the different measuring techniques, for a wide range of ionic strength and composition of the water phase and two crude oils.   

Effects of Electric Fields on Coalescence of Drops at Planar Interfaces

Although electro-coalescence has applications in such fields as oil purification, lab on a chip, and mass spectroscopy, the dynamics involved within it are not fully understood. In series of experiments, we investigate the effects of an electric field on coalescing fluid bodies. A neutrally-charged droplet is deposited inside a layer of silicone oil slightly above a planar silicone oil-drop fluid interface. By introducing a DC electric field, we apply additional forces to the interface and droplet. In most cases, the presence of the electric field causes the droplet to initiate coalescence. The effect of this additional field in conjunction with the effect of other physical properties of liquids such as viscosity and interfacial tension are studied by utilizing a digital high-speed camera. The characteristics of this phenomenon are compared with those of equivalent systems in absence of the electric field.   

Destabilization of Pickering emulsions using external electric fields

It is known that emulsions can be stabilized by the presence of particles which get trapped at fluid-fluid interfaces and prevent adjacent drops from coalescing with each other. We show here that such emulsions, or Pickering emulsions, can be destabilized by applying external electric fields. This is demonstrated experimentally by studying water drops in decane and using various types of particles, including micro and nanoparticles. It is conjectured that the destabilization occurs due to the motion of particles on the surface of drops in presence of a uniform electric field. Although there should be no electrostatic forces acting on neutral particles in a uniform electric field, the presence of the drop itself introduces some non-uniformity which is responsible for particle motions along the surface. Particles translate either to the poles or equator of the drop, depending on the relative dielectric constants of the particles, the surrounding fluid and the fluid within the drop. Such motions break the particle barrier, thus allowing for drops to merge into one another.   

Spreading Process of a Drop in Electrowetting

Spreading process of a conducting drop by electric field is called the electrowetting, which is derived by the electrical force concentrated on the three-phase contact line (TCL). During the spreading process, the shape of the drop changes dynamically, and the transient behavior of the drop becomes more complicated due to the contact line friction and the capillary force acting on TCL. In the present work, the shape mode equations are developed to describe the dynamic evolution of the shape of the drop. The small deformation from spherical shape and the weak viscosity of the liquid are assumed to apply the domain perturbation method. The normal stress balance and the dynamical contact angle model are unified as single boundary condition, which distinguishes our method from others. The electrical, capillary, and contact line friction forces concentrated on the TCL are approximated by using the delta function. The derived shape mode equations show a relatively good agreement with experiments.   

Session LH: Waves

A Parametric Investigation of Breaking Bow Waves using a 2D+T Wave Maker

An experimental study of bow waves generated by a 2D+T (Two Dimensions plus Time) wave maker in a tank that is 14.8 m long, 1.2 m wide and 2.2 m deep is presented. Rather than simulating a specific ship hull, here we use a parametric set of wave maker motions with each parameter simulating a common feature of a ship hull form. Three categories of wave maker motions are used: ``slap'' (rotation of the wave board (held flat) about the keel), ``fixed'' (translation the wave board while it is upper part remains flat and at a fixed angle relative to horizontal), and ``full'' (simultaneous rotation and translation). The wave maker motions are run over a range of speeds and, in the ``fixed'' cases, over a range of angles. The temporal histories of the wave profiles were measured using a cinematic LIF technique. The relationship between various geometrical features of the waves and the wave maker motion parameters is explored. Each category of wave maker motions produces waves that develop and break in markedly different ways, thus highlighting the complex nature of bow waves. The wave crest speeds vary between 2 and 2.5 times the maximum speed of the wave maker and, for a given class of wave maker motion, vary with wave maker speed.   

The Cross-Stream Structure of the Crests of Breaking Waves

Surface profiles and flow fields in the crests of breaking waves are usually measured in vertical stream-wise planes. However, measurements of the turbulent flow in boundary layers along flat rigid walls have indicated the importance of streamwise flow structures. In the present study, breaking waves are examined in a tank that is 12.8 m long and 1.2 m wide with a water depth of 0.91 m. A programmable wave maker is used to generate wave packets (central frequencies 1.15 - 1.42 Hz) that create breakers by dispersive focusing. Different amplitudes of the wave maker motion are used to generate various breaking waves ranging from weakly spilling to plunging breakers. A cinematic 2D LIF technique is used to measure the crest profile histories and the light-sheet plane is oriented to measure both the stream-wise and cross-stream crest profiles in separate experiments. It is found that the development of ripples due to turbulence-free surface interactions is highly repeatable and that even though the waves are two-dimensional before breaking, the amplitude of the cross-stream components quickly reaches 50{\%} of the stream-wise ripple amplitude.   

Unstable internal waves

Recent advancements in observational techniques have revealed that internal gravity waves are an ubiquitous phenomena in the ocean and in the atmosphere. In particular, internal waves propagating in a strati?ed ocean have been observed and reported to have large amplitudes. Understanding the breaking mechanisms of these waves is crucial for explaining mixing and transport phenomena within the ocean. As experimental observations show, for near two layer stratification, waves become unstable in large amplitude regimes and the wave-breaking closely resembles Kelvin Helmholtz shear instability originating in the maximum displacement of the pycnocline region. The instability is modulated by the stream-wise variation of the shear. We simulate numerically the generation and propagation of solitary waves starting from a step function initial condition and monitor the wave-induced shear instabilities. A conservative projection method for the variable density Euler equations is implemented in this scope. The code is validated against experimental data as well as theoretical results. In an effort to elucidate whether the instabilities are an intrinsic property of the wave or they are induced by the experimental generation, we study the time evolution of traveling wave solutions.   

Weakly nonlinear, multi-modal evolution of wind-generated long internal waves in a closed basin

A weakly nonlinear evolution model that accounts for multi-modal interaction in a continuously stratified lake of variable depth is derived. The model for the first two vertical modes in a lake that is subject to wind stress forcing is numerically simulated. Defining modal energies, energy transfer between the first and the second vertical modes is calculated for several different forms of the density stratification. Modal energy transfer mainly occurs during reflection of mode-one waves at the vertical end walls, and it is shown that the amount of energy transfer from the first to the second mode is greatly dependent on the shape of the stratification. Also, the initial modal energy partition at the end of the wind setup is shown to depend significantly on the penetration depth of the wind stress, especially if the stress distribution extends into the upper levels of the metalimnion.   

Corner waves downstream a partially submerged vertical plate

We have studied experimentally and numerically the expansion flow developing downstream the corner of a partially submerged vertical plate. In this flow configuration, a steady wave remains attached to the corner of the plate. Both the amplitude and slope of the wave front increase with the downstream distance until, the wave breaks resulting in either a spilling or a plunging breaker. Following theoretical considerations, we propose a criterion based on a critical Froude number to determine which breaker configuration prevails. This criterion is shown to be in good agreement with the experimental results. Despite the simplicity of this flow, the observed wave pattern is remarkably similar to that one found at a dry stern in high-speed surface vessels.   

Experimental investigation of power capture from pitching vertical cylinders in irregular waves

Point absorbers are one of the main categories of wave energy converters being developed worldwide. These devices are classified by their dominant mode of motion relative to the water surface. Most of these converters use either a hydraulic system or direct drive electric generator as a means for power take-off (P.T.O.). These wave energy devices are highly suitable for intermediate depth locations. This paper presents the results from an experimental study on the power capture of bottom-pivoted pitching cylinders in intermediate water depth subjected to regular and irregular waves. All experiments were conducted in the University of Sydney's wave flume. The geometry of the pivoted cylinder, external damping and additional inertia (to simulate the impact of water ballasting) were taken as variable parameters in order to optimize the power capture efficiency in different wave conditions. The devices were subjected to a realistic wave climate obtained from the analysis of on-site buoy measurements from the European Marine Energy Center in Scotland, a location renowned for its wave energy potential, where existing devices have been already tested.   

Pattern selection in a horizontally vibrated container

We investigate the dynamics and pattern formation properties of a fluid interface whose supporting container is subjected to horizontal vibrations. Experimental results demonstrate the prevalence of so-called subharmonic cross-waves beyond the linear stability limit of directly forced synchronous surface waves, and reveal several new and interesting properties of these subharmonic waves in large aspect ratio systems, including a preferred orientation other than 90 degrees, a tendency to form domains of distinct patterns, and a variety of low-frequency modulations.   

Axisymmetric Weakly Compressible Transient Pipe Flow and Water Hammer Control

Despite the partial success of existing theoretical models in explaining certain transient water flow phenomena in a long pipe, they can hardly predict the evolution of strong water hammer, in particular the one downstream the valve caused by its closing (reversed water hammer). We attack this important problem by a new perturbation theory based on the unsteady axisymmetric and compressible Navier-Stokes equations. The leading-order transient solution is~in excellent agreement with the direction simulation of the original N-S equation. We establish a simple relation~between the valve motion and adjacent pressure in reversed water hammer, by which the strategy of optimal control of reversed water hammer is analyzed and illustrated.   

Instabilities of coupled wave packet systems

Propagation of wave packets in layered or continuously stratified fluids will typically lead to coupled, nonlinear Schrodinger equations (CNLS). The competition between dispersion and nonlinearity will be crucial. A novel instability can arise from cross phase modulation (XPM), or the effect on a wave packet due to the presence of the other one. XPM in the hydrodynamic context is now considered from several perspectives. In the long wave regime governed by the extended Korteweg de Vries system, CNLS are derived by multiple-scale expansions and modulation instabilities (MI) of plane waves are studied. This will reveal new energy transfer mechanism. Secondly, from a scientific perspective, special, integrable higher order CNLS are considered and the presence of MI is examined. This is critical as higher (or fourth) order effects must be considered when the wave slope is sufficiently large.   

Session LJ: Bio-Fluids: General II

Recent progress on Modeling the Human Tear Film

We report on recent results in from our modeling efforts to better understand the dynamics of the human tear film. Lubrication theory is used to reduce the problem to a nonlinear one-dimensional partial differential equations governing the tear film thickness. The curvature variation of the (ellipsoidal) cornea is studied in a model problem that illustrates the influence of this aspect of the eye. Other progress will be discussed as available, including a shear thinning fluid to model tears.   

Human Tear Film Dynamics with an Overset Grid Method

We present recent progress in the understanding of the dynamics of the human tear film on the complex eye-shaped geometry. The evolution is modeled during relaxation (after a blink) using lubrication theory and the effects of viscosity, surface tension and gravity are explored. The highly nonlinear governing partial differential equation is solved on an overset grid by a method of lines coupled with finite differences. Our two-dimensional simulations, calculated in the Overture framework, recover features seen in one-dimensional simulations and mimic some experimental observations like hydraulic connectivity around the lid margins.   

The elasto-pipette: grabbing water with thin elastic sheets

Py \emph{et. al.} [1] have recently shown that the coupling between surface tension and elasticity of thin sheets can be used to induce self-assembly of flat elastic objects into three dimensional structures: \emph{capillary origami} at play. We here present the results of a combined experimental and theoretical investigation of a related system in which a thin elastic petal-shaped plate is withdrawn from the flat interface of a liquid bath. As the plate is drawn upwards, it deforms due to interfacial and hydrostatic forces, up to a point where it completely detaches from the interface. If the bending stiffness of the plate is sufficiently low, upon detachment a regime can be attained where the petal-shaped plate can fully enclose and therefore \emph{grab} a drop from the liquid bath. We propose this mechanism as a robust means by which to manipulate and transport small fluid droplets. \noindent [1] C. Py, P. Reverly, L. Doppler, J. Bico, B. Roman and C. Baroud, \emph{Phys. Rev. Lett.} \textbf{98}, 156103 (2007).   

Wetting of textured hydrophobic surfaces

Water repellency in nature and technology typically results from textured hydrophobic surfaces. The roughness elements of such surfaces typically have edges that pin the contact lines of advancing droplets. We present the results of a numerical investigation that relates the contact angle hysteresis and adhesive force to the geometrical, wetting, and elastic properties of the substrate. A number of generic surfaces are considered, including carbon nanotube forests, nano gratings, and insect cuticle. The calculated wetting properties are used to predict common observable quantities such as the critical tilt angle for drop motion.   

Flow Measurements over Embedded Cavities Modeling the Microgeometry of Bristled Shark Skin

Certain species of sharks (e.g. shortfin mako) have a skin structure that results in a bristling of their denticles (scales) during increased swimming speeds. This unique surface geometry results in the formation of a 3D array of cavities\footnote{Patent pending.} (d-type roughness geometry) within the shark skin, thus causing it to potentially act as a means of boundary layer control. In order to further understand the effectiveness of this complex geometry, ProE was used to replicate the bristled shark skin of the shortfin mako using a rapid prototyping machine. Two simplified geometries of the shark skin, including 2D transverse cavities and a 3D array of staggered cavities, were also studied. Boundary layer measurements using DPIV were obtained and compared for all three geometries. Of particular interest is the role that the riblets, on the face of the denticles, appear to play in forming an organized array of embedded vortices within the surface.   

Suppression of shocked-bubble dynamics by tissue confinement

Estimates are made of the effect of confinement by tissues on the action of small bubbles when subjected to strong pressure waves. The applications of interest are biomedical procedures involving short strong ultrasound bursts or weak shocks of the kind delivered in shock-wave lithotripsy. Confinement is anticipated to be important in suppressing mechanical injury and slowing the rate of its spread. We consider bubbles in a liquid such as blood within a small vessel in the tissue. A generalization of the Rayleigh-Plesset equation allows us to estimate the effect of the elasticity and viscosity of the surrounding tissue. Ranges of soft-tissue properties are estimated from a variety of different measurements available in the literature. Solutions suggest that elasticity is insufficient to significantly alter bubble dynamics but that viscosities from the mid-to-high range of those suggested might play a significant role in suppressing bubble action. Simulations in two space dimensions of a shocked bubble in a water-like fluid interacting with a viscous material show that the much more complicated bubble jetting dynamics in this configuration are also significantly suppressed. The dynamics of this suppression are investigated.   

Wheat field and Dominoes

Once perturbed, an alignment of identical slender elements can either oscillate around an equilibrium position and propagate waves (wheat field limit) or destabilise and propagate a shock (dominoes limit). In the wheat field limit, we show that two kinds of waves can be observed depending on the intensity of the forcing wind. In the dominoes limit we study the shape of the shock and show that its velocity only depends on the height of a domino and on the spacing between the different elements.   

Impingement of Ring Vortices on a Wall - a Comparison of Experiments and Computations

The descending disk experiments of Kubota et al. (2008) generate ring vortices that impinge upon the floor and travel outward from the disk. These vortices do not exhibit some of the complex behavior that is found in the simulations of Khalifa and Elhadidi (2007) and DeGraw and Cimbala (2006). Among the leading candidates for the differences between the simulations and the experiments is the possible presence of turbulence in the experiment that is not present in the simulations. To study this possibility, we numerically simulate the related but simpler case of an axisymmetric ring vortex impinging upon a plane wall as both a laminar and a turbulent flow. In the laminar case, the primary vortex induces separation vortices that are periodically ejected from the surface and tend to stop growth of the primary vortex. In the turbulent case, we find that while a separation vortex may develop, it tends to be smaller and no ejection takes place. We simulate a variety of cases in which we turn turbulence on or off (in the form of the $k-\epsilon$ turbulence model), and find that the ejection-type behavior is present only in the laminar solutions, while the turbulent cases typically exhibit a primary vortex that continues to grow radially. This turbulent behavior is similar to that observed by Kubota et al., and implies that their descending disk flow is at least partially turbulent.   

Session LK: Nano-Fluids I

Thermal Resistance at the Liquid-Solid Interface

Heat conduction between parallel plates separated by a thin layer of liquid Argon is investigated using three-dimensional MD simulations employing 6-12 Lennard-Jones potential interactions. Channel walls are maintained at specific temperatures using a recently developed interactive thermal wall model. Heat flux and temperature distribution in nano-channels are calculated for channel heights varying from 12.96 nm to 3.24 nm. Fourier law of heat conduction is verified for the smallest channel, while the thermal conductivity obtained from Fourier law is verified using the predictions of the Green-Kubo theory. Temperature jumps at the liquid/solid interface, corresponding to the well known Kapitza resistance, are observed. Using systematic studies thermal resistance length at the interface is characterized as a function of the surface wettability, thermal oscillation frequency, wall temperature, thermal gradient and channel height. An empirical model for the thermal resistance length, which could be used as the jump-coefficient of a Navier-type boundary condition, is developed.   

Slip flow: How slip occurs on a two-dimensional surface

The relative interfacial velocity between a liquid and solid is called slip. Though there are physical measurements and numerical computations of the amount of slip, the mechanics of slip remain unclear. For 2D flows (i.e. over a 1D surface) slip occurs by the propagation of defects along the surface.\footnote{A. Martini, A. Roxin, R. Q. Snurr, Q. Wang {\&} S. Lichter. \textit{J. Fluid Mech.} \textbf{600}: 257-269 (2008).} Here, we show how slip occurs in 3D flow using molecular dynamics (MD) simulation. We study slip in a long Couette channel of fixed height with molecules of size $\sigma $. We carry out a sequence of MD simulations beginning with a 2D computational geometry, i.e. width = $\sigma $, and incrementally increase the width of the computational domain. By examining the dynamics at the liquid/solid interface, we can follow the propagation of interfacial defects, as they evolve from their well-understood 1D form into fully 2D slip. Does slip on 2D surfaces also occur through the propagation of defects as it does over a 1D surface? We hope to answer that question in this presentation. The results of this work have application to optimizing surfaces for slip and to flows in small geometries, such as carbon nanotubes and in tribological flows.   

A mechanism based on fluid compressibility to explain molecular scale slip behavior

We reproduce molecular scale slip behavior by solving continuum equations for the shear flow of a \textit{compressible} fluid between two walls \textit{in the presence of wall potentials}. A constant slip length is obtained at low shear rates which transitions, at a critical shear rate, to a different constant slip length at high shear rates. This is consistent with molecular dynamic (MD) results. The critical shear rate for transition can be estimated based on scaling arguments. The numerical results motivate a theoretical solution, based on continuum equations, for the slip lengths at high and low shear rates. Prior MD results can be consolidated in the context of this model, and it also elucidates the mechanism of slip. It is seen that at low shear rates the fluid experiences an additional body force due to the wall potential (e.g. Lennard-Jones potential). This slows down the fluid in the first molecular layer. This body force is non-zero only if the fluid is compressible. At high shear rates this body force is negligible and the slip length is determined by a friction coefficient between the wall and fluid molecules.   

Identification of concentration polarization regimes in microchannel-nanochannel interfaces using method of characteristics

We developed a simple transport model to study concentration polarization (CP) regimes in microchannel-nanochannel interfaces. The models include advection due to electroosmosis, pressure-driven flow, electro migration, and diffusion. The electric double layer effects are assumed to be confined to near wall regions. This model is used to study CP in a series microchannel-nanochannel-microchannel geometry and found to provide significant insight into dynamics of CP. Consistent with experimental observations, two different CP regimes are identified: In one regime CP enrichment and depletion zones remain local to the channel interfaces (CP without propagation). In another regime, CP zones show long range propagation in the form of concentration shocks (CP with propagation). Solutions based on the method of characteristics are shown to uniquely determine which CP regimes will be selected by the system. We find propagation of CP is determined by two major system parameters: a nanochannel Dukhin number, and the ratio of the co-ion mobility to electroosmotic mobility. We found that after CP propagates, the system cannot be affected by perturbations to the reservoir. Extension of this model to more complex geometries will be discussed.   

Improved potential of mean force for Brownian dynamics simulation of nanoparticle aggregation

Aggregation of nanoparticles in liquid suspension is a phenomenon that affects the design and scale-up of process equipment for nanoparticle synthesis. The radial distribution function of nanoparticle pairs is an essential statistic characterizing multiparticle dynamics that must be captured by Brownian dynamics (BD) simulations in order to accurately simulate the structure of nanoparticle aggregates. Molecular dynamics (MD) simulations of a model aggregating system are used as a benchmark to evaluate the simplest specification of the potential of mean force (PMF) in BD, which yields good agreement in the diffusion-limited regime but performs poorly in the reaction-limited regime. An improved potential of mean force that accounts for the relative acceleration between nanoparticles due to the presence of solvent molecules is developed. Implementation of this improved PMF in BD yields promising preliminary results for the structure of nanoparticle aggregates when compared with benchmark MD simulations.   

Diffusivity effects on charged species separation in nanochannels

Recent work has investigated the dispersion and separation of charged molecules in nanochannels. One conclusion has been that the combination of transverse velocity and electric field gradients can provide a mechanism for separation of different-valence ionic species. Building on this, we present a continuum transport model for finite-sized particles in a nanofluidic system and analyze the model both theoretically, with Taylor-Aris dispersion theory, and computationally, with direct numerical simulation. We assume a finite-sized electric double layer, a dilute solution, and an axially applied DC electric field. We show that, under these conditions, finite-sized particles may exhibit qualitatively different separation behavior than predicted by small ion theory.   

Spreading of a Nanodroplet on a Solid Surface Physically-Patterned with an Array of Pillars

Molecular dynamics simulations are used to study the spreading dynamics of a Lennard-Jones liquid droplet on a heterogeneous solid surface. The solid is physically patterned by placing a set of pillars of square or circular cross section on an otherwise flat surface. The liquid-solid interaction is modeled by a modified Steele's potential derived for arrays of pillars characterized by a desired roughness and solid fraction. Using the modified Steele's potential, liquid-solid interactions can be computed more quickly, and larger droplet sizes can be studied. Simulations indicate that the spreading of nanodroplets depends not only on the surface energy of the solid, but also on the heterogeneity of the solid surface. For a constant solid surface energy, the topographic structure of the solid surface can have a significant effect on its hydrophobic characteristics. By varying the pillar height, spacing, and arrangement on the solid surface, a transition between the Wenzel and Cassie modes of wetting is observed in the simulations. These observations are explored in terms of the interplay between the bulk liquid chemical potential and the liquid-solid interfacial tension, as well as the topology of the liquid-solid potential-energy surface induced by surface heterogeneity.   

Particle dynamics and rheology of SWNT suspensions under shear and electric fields

The net orientation angle of single-wall nanotubes (SWNTs) in liquid suspension under combined shear flow and electric fields is investigated experimentally with an optical polarization-modulation technique. The macroscopic viscosity of the suspension under the shear and electric fields is also measured simultaneously to the optical measurement. Theoretical predictions of the time scales of two particle-dynamics processes, the orientation of particles and the formation of microstructure in the suspension, are compared with experimental data. The relation between the particle dynamics and the macroscopic rheology of the dilute SWNT suspension is discussed.   

High-speed Tracking of Quantum Dots in Microflows using Evanescent Wave Illumination

Total internal reflection velocimetry (TIRV) is applied to measure the dynamics of colloidal quantum dot (QD) tracer particles within 200 nm of a microchannel wall at shear rates in excess of 20,000 s$^{-1}$. QDs are quickly developing into viable tracer particles for measuring microscale fluid dynamics. However, the low emission intensities of QDs usually require long exposure and inter-frame times, which limit velocity resolution and compromise accuracy (due to their fast diffusion as a consequence of a small, 17 nm hydrodynamic diameter). In this study, a two-stage, high-speed image intensifier and camera were integrated into an evanescent wave microscopy imaging system to provide the necessary high temporal resolution to image the fast diffusion dynamics of QD's in real time (up to 10,000 fps), which allowed individual particles to be tracked continuously for extended periods. In addition to examining the trajectories of individual particles, ensemble-averaged tracking measurements reveal near-wall velocity distributions in high-speed microchannel flows (Re$\sim $10), where velocities on the order of 5 mm/s are measured within 200 nm of the microchannel wall. This data provides a robust confirmation of recent results demonstrating diffusion-induced bias error for near-wall velocimetry.   

A Universal AC Cone Angle due to Net Entrainment of Anionic Species

The slender conical meniscus that is obtained by the application of high frequency AC field is quite distinct from DC Taylor cone. The AC cone shows continuous longitudinal growth and has a much smaller half cone angle of $\sim 11^{\circ}$. Mass spectrometry on the microjet from the AC cone shows that dissociation reaction occurs at the tip but only the low-mobility anionic species are entrained to produce a charged cone. These free negative charges relax to the interface to produce a non-uniform surface charge density that scales with respect to the azimuthal radius as $\rho ^{-\textstyle{1 \over 2}}$ to balance the singular normal capillary pressure. Repulsion of this entrained surface charge and the Maxwell pressure they induce are estimated with an elliptic integral and a variational formulation produces a normal stress balance with capillary pressure that is only satisfied at a universal angle of $12.6^{\circ}$ for the liquids with high dielectric constant, in good agreement with the measured values for the organic solvents used in experiments.   

Session LL: Bio-Fluids: Wakes and Mixing I

LCS analysis of a biologically inspired wake

Particle Image Velocimetry (PIV) was used to investigate the wakes of rigid pitching panels with a trapezoidal panel geometry, chosen to model idealized fish caudal fins. Experiments were performed for Strouhal numbers from 0.23 to 0.65. The three dimensional flow field around the panel is reconstructed by integrating two-dimensional PIV results across the volume surrounding the panel. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von K$\acute{a}$rm$\acute{a}$n vortex street pattern was observed along the mid-span of the near wake, but the complexity and three-dimensionality of the wake increases away from the mid-span as streamwise vortices interact with the swept edges of the panel.   

The Hydrodynamic Wake of Two Species of Swimming Krill

Krill are often found in unorganized swarms or coordinated schools depending on the species. To test if group organization is related to the hydrodynamic wake produced by swimming krill we quantified the flow structure in the wake of \textit{Euphausia superba, }a schooling Antarctic krill, and \textit{Euphausia pacifica, }a swarming Pacific krill. In this study, we used infrared Particle Image Velocimetry (PIV) to analyze the structure of the hydrodynamic disturbance of free-swimming individual specimens. The downward directed jet produced by \textit{E. pacifica }has a lower maximum velocity (3.4 +/- 1.1 cm/s vs. 6.2 +/- 1.3 cm/s), has a steeper wake angle (59 +/- 20 degrees vs. 48 +/- 14 degrees), and decays faster (0.3 s vs. 0.6 s) than the jet of \textit{E. superba}, which suggests that the wake is less persistent for signaling in the smaller krill species (\textit{E. pacifica}). Time record analysis reveals that the wake flow is very weak beyond 0.5 body length for \textit{E. pacifica} and beyond 1 body length for \textit{E. superba}. Since \textit{E. superba} separation distances within a school range from 1 to 3 body lengths (from previous data), it appears that \textit{E. superba} may not be using solely the hydrodynamic signal to facilitate schooling.   

Mixing efficiency of swimming animals in stratified fluids

The potential role of animal-fluid energy interactions in ocean mixing is a topic of increasing study that has been limited by the need for data at the scale of individual animals. Previous findings suggest that the energetic input by swimming animals to the ocean mixing energy budget may impact mixing at the same level as winds and tides, whose respective rates of kinetic energy dissipation are of the same order of magnitude. However, these results equate dissipation of mechanical energy with mixing; not all mechanical energy that is dissipated goes into mixing a fluid. The mixing efficiency should instead be an indicator of mixing. We present a method to determine the mixing efficiency of swimming animals that combines the techniques of DPIV, PLIF and dye visualizations. This methodology is then applied to multiple swimming cycles of \textit{Aurelia labiata} to answer whether mechanical energy at small animal scales can achieve any substantial mixing before it is dissipated as heat.   

A fluid mechanical model for current-generating-feeding jellyfish

Many jellyfish species, e.g. moon jellyfish \textit{Aurelia aurita,} use body motion to generate fluid currents which carry their prey to the vicinity of their capture appendages. In this study, a model was developed to understand the fluid mechanics for this current-generating-feeding mode of jellyfish. The flow generated by free-swimming \textit{Aurelia aurita} was measured using digital particle image velocimetry. The dynamics of prey (e.g., brine shrimp \textit{Artemia}) in the flow field were described by a modified Maxey-Riley equation which takes into consideration the inertia of prey and the escape forces, which prey exert in the presence of predator. A Lagrangian analysis was used to identify the region of the flow in which prey can be captured by the jellyfish and the clearance rate was quantified. The study provides a new methodology to study biological current-generating-feeding and the transport and mixing of particles in fluid flow in general.   

Flow field around \textit{Vorticella}: Mixing with a reciprocal stroke

\textit{Vorticella }is a stalked protozoan. It has an extremely fast biological spring, whose contraction is among the fastest biological motions relative to size. Though the \textit{Vorticella }body is typically only 30 $\mu $m across, the contracting spring accelerates it up to speeds of centimeters per second. \textit{Vorticella }live in an aqueous environment attached to a solid substrate and use their spring to retract their body towards the substrate. The function of the rapid retraction is not known. Many hypothesize that it stirs the surrounding liquid and exposes the \textit{Vorticella }to fresh nutrients. We evaluate this hypothesis by modeling the \textit{Vorticella }as a sphere moving normal to a wall, with a stroke that moves towards the wall at high Reynolds number, and away from the wall at low Reynolds number. We approximate the flow during contraction as potential flow, while the flow during re-extension is considered Stokes flow. The analytical results are compared to the flow field obtained with a finite element (Comsol Multiphysics) simulation of the full Navier-Stokes equations.   

Instabilities, pattern formation and mixing in active suspensions

Suspensions of self-propelled particles are known to undergo complex dynamics as a result of hydrodynamic interactions. To elucidate these dynamics, a kinetic theory is developed and applied to study the linear stability and the non-linear pattern formation in these systems. The evolution of a suspension of self-propelled particles is modeled using a conservation equation for the particle configurations, coupled to a mean-field description of the flow arising from the stress exerted by the particles on the fluid. Based on this model, the stability of isotropic suspensions of particles is first investigated. We demonstrate the existence of an instability in which shear stresses are eigenmodes and grow exponentially at long scales, and propose an interpretation in terms of the system entropy. Non-linear effects are also studied using numerical simulations in two dimensions. These simulations confirm the results of the stability analysis, and the long- time non-linear behavior is shown to be characterized by the formation of strong density fluctuations, which merge and break up in time in a quasi-periodic fashion. These complex motions result in very efficient fluid mixing, which we quantify by means of a multiscale mixing norm.   

Bacterial chemotaxis in the ocean: microfluidic studies

Bacteria are key players in the biogeochemistry of the ocean. We present microfluidic experiments to mimic nutrient conditions experienced by marine bacteria. Using videomicroscopy, we quantified the intensity and time scale of the response of bacteria to nutrient pulses. We found that marine bacteria are capable of superior chemotaxis compared to {\em Escherichia coli} (the classic model of chemotactic motility), likely an adaptation to the ephemeral nutrient conditions in the ocean. For moving nutrient sources, performance depends on the speed of the source: we present the first experimental evidence that marine bacteria can colonize plumes of marine snow particles, for slow to moderate particle settling speeds. Finally, preliminary numerical results reveal that turbulence can play a significant role in bacterial foraging in the ocean.   

Life at high Deborah number

Many biologically-relevant situations in cell locomotion involve non-Newtonian fluids. Important examples include the motion of spermatozoa in cervical mucus, or the movement of bacteria in biofilms. In this work, we present quantitative models of cell locomotion in polymeric solutions by deriving integral theorems which allow a general determination of the swimming kinematics of a small-amplitude swimmer for arbitrarily large Deborah numbers.   

Waltzing {\it Volvox\/}: Orbiting Bound States of Flagellated Multicellular Algae

The spherical colonial alga {\it Volvox} swims by means of flagella on thousands of surface somatic cells. This geometry and its large size makes it a model organism for the fluid dynamics of multicellularity. Remarkably, when two nearby colonies swim close to a solid surface, they are attracted together and can form a stable bound state in which they continuously waltz around each other. A surface-mediated hydrodynamic attraction between colonies combined with the rotational motion of bottom-heavy {\it Volvox} are shown to explain the stability and dynamics of the bound state. This phenomenon is suggested to underlie observed clustering of colonies at surfaces.   

Can unicells increase their nutrient uptake by swimming?

We introduce two simple models for the flow generated by a self-propelled flagellate: a sphere propelled by a cylindrical flagellum and one propelled by an external point force. We use these models to examine the role of advection in enhancing feeding rates in 3 situations: (i) osmotroph feeding on dissolved molecules, (ii) interception feeding flagellates feeding on non-motile prey particles, and (iii) interception feeders feeding on motile prey (such as bacteria). We show that the Sherwood number is close to unity for osmotrophic flagellates, as suggested by most previous models. However, a more correct representation of the flow field than that predicted by a naive sinking sphere model leads to substantially higher clearance rates for interception feeding flagellates. We finally demonstrate that prey motility significantly enhances prey encounter rates in interception feeding flagellates and in fact often is much more important for food acquisition than the feeding current.   

No many-scallop theorem: Collective locomotion of reciprocal swimmers

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. However, there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field.   

Session LM: Sheared Granular Matter and Granular Collapse

The response of dense dry granular material to the shear reversal

We have performed two dimensional granular experiments under pure shear using bidisperse photo-elastic disks. Starting from a stress free state, a square box filled with granular particles is subject to shear. The forward shears involved various number of steps, leading to maximum strains between 0.1 and 0.3. The area is kept constant during the shear. The network of force chains gradually built up as the strain increased, leading to increased pressure and shear stress. Reverse shear was then applied to the system. Depending on the initial packing fraction and the strain at which the shear is reversed, the force chain network built prior to the shear reversal may be destroyed completely or partially destroyed. Following the force chain weakening, when the reserve shear is continuously applied to the system, there is a force chain strengthening. Following each change of the system, contact forces of individual disks were measured by applying an inverse algorithm. We also kept track of the displacement and angle of rotation of every particle from frame to frame. We present the results for the structure failure and reconstruction during shear reversals. We also present data for stresses, contact force distributions and other statistical measures.   

Slow Shear of Non-Spherical Particles

We probe the microscopic properties of granular materials consisting of ellipsoidal particles. The aim of these studies is to understand the role played by particle shape. The experiments are carried out in 2D and consist of pure shear with maximum strains up to 0.3, followed by reverse shear. The particles are made of a photoelastic material, so that we can determine particle-scale forces as well as particle displacements, rotations and orientations. We present results for the stresses, strains, contact forces, etc.   

Boundary stresses due to sheared granular mixtures

Models for stress produced by a sheared granular layer indicate stress should scale with particle size (such as the classic model suggested by Bagnold in 1954 where stress scales as particle size squared [1]). However, it is not clear how this particle-size scaling should be modified for a mixture of different-sized particles, important for applications such as debris flows. We investigate external stresses generated by a dense sheared granular mixture flowing in a thin layer over a solid boundary. To do so, we use Distinct Element Method (DEM) simulations based on a soft sphere model and compare the results with large-scale experimental measurements. Based on results from a variety of mixtures of different-sized particles, we have found that the scaling of the stress at the boundary does not depend on a simple metric such as average particle size. Instead, the scaling of the stress appears to have a more complicated dependence on both the relative sizes of the particles in the mixture and the relative concentration of the different species. [1]R.A. Bagnold (1954) Proc. R. Soc. Lond., A 225 pp. 49-63.   

Green function measurements in the bulk of the 2D granular systems

We have performed experiments to measure the Green function responses to local perturbations in the bulk of the 2D granular systems using photo-elastic disks. The local perturbations were created in several different ways by applying pulling forces along a fixed direction, by applying forces pushing uniformly outwards, and by removing individual particles from force chains. Responses of systems were studied at different packing fractions for systems under isotropic compression and pure shear. We will present the results from the measurements of contact forces, particle displacement and rotation, and force chain networks.   

Stick-Slip and Granular Force Networks: A Statistical Description

We probe the nature of granular friction and stick-slip using a novel apparatus that combines photoelastic response at the grain scale, and quantitative measurements of pulling force and kinematics. In the experiments, a slider is pulled across the surface of a granular layer consisting of photoelastic particles. A pulling device moves at constant velocity, $V$, and acts on the slider through a spring of constant $k_s$. Non-periodic stick-slip motion results. During stick, the spring loads up, and the force network of the granular material evolves steadily. Slip is preceded by a creep regime involving small rearrangements of the force network. Slip is rapid and consists of one or more 'force chain' failures. Most properties, including energy losses at slip, forces at failure and immediately after slip, slipping times, etc. are characterized by broad distributions. For instance, the slip energy losses, in analogy to the Gutenberg-Richter law for earthquakes, has a probability distribution function that varies as a powerlaw in $\Delta E$ with and exponent of $\epsilon = 1.2 \pm 0.1$ The detailed motion of the slider during a slip event may be quite complex, as individual force chains fail, and new chains form to take their place. We present details of distributions and we relate our observations to expectations from a simple friction model and to an elastic failure model. We appreciate input from Paul Johnson (LANL) and Chris Marone (Penn State University).   

Non-linear and linear wave propagation in booming sand dunes

For centuries booming sand dunes have intrigued travelers and scientists alike. These dunes emit a persistent, low-frequency sound during a slumping event or natural avalanche on the leeward face of the dune. This sound can last for several minutes and be audible for miles. The acoustic emission is characterized by a dominant audible frequency (70 - 105 Hz) and several higher harmonics. In the work of Vriend et al. (2007), seismic refraction experiments show the existence of a multi-layer internal structure in the dune, which acts as a waveguide for the acoustic energy. The waveguide channel, within the subsurface structure of the dune, amplifies the sound and determines the booming frequency. The recorded booming frequency depends directly on the spatial dimension of the natural waveguide. The current study presents additional insight in the wave propagation characteristics. The source of the acoustic emission is burping sand - sand with a narrow particle size distribution that emits short broadband squeaks (50 - 100 Hz) upon direct shearing of the grains. The burping emission displays non-linear and dispersive effects in its wave propagation characteristics during field experiments. The emission cannot develop into the loud, sustained booming without the proper subsurface structure.   

Influence of volume fraction on the dynamics of granular impact

Variation of the volume fraction $\phi$ of non-cohesive granular media causes disproportionate changes in the forces exerted on impacting objects and, consequently, the impact kinematics. In our experiments, a computer controlled air fluidized granular bed is used to vary $\phi$ from 0.58 (low) to 0.62 (high) for 0.3~mm diameter glass spheres and \~1~mm poppy seeds. An accelerometer attached to a 4.0~cm diameter steel sphere measures collision forces for initial impact velocities ranging from 0.5 to 3.5~m/s. As an example of the dramatic changes produced by varying $\phi$, time series of the force during impact with poppy seeds at an impact velocity of 1~m/s change from monotonically increasing with slope 100~N/s at $\phi=0.59$ to monotonically decreasing with slope -100~N/s at $\phi=0.62$; glass beads show similar behavior. Increasing $\phi$ from low to high at fixed collision velocity causes the penetration depth to decrease monotonically by approximately 50\%. However, for the same parameters, the collision duration changes little, decreasing by $\approx 10$\% as $\phi$ is increased from 0.58 to $\approx 0.6$ and then increasing by about 3\% as $\phi$ is increased to 0.63. Our impact simulations exhibit the same collision dynamics vs.\ $\phi$ and reveal qualitative differences in grain velocity fields and local volume fraction changes between low and high $\phi$ states. Support by the Burroughs Wellcome Fund and the Army Research Lab MAST CTA.   

The effect of particle shape in the collapse of a granular column

Some previous experiments on the collapse of a granular column have reported that the shape of the grains has little influence in the collapse process and the shape of final deposit. In contrast, other studies indicate that the flow of long grains has a very different behavior than that of simple grains. To investigate this apparent discrepancy, we performed Discrete Element (DE) simulations of the collapse of 2D granular columns under the action of gravity. In contrast to similar previous investigations, we consider elongated grains formed by constraining several individual particles on a straight line. The main parameter used to describe the final state of the deposit is the aspect ratio, $a$, of initial height ($H_0$) to initial radius ($R_0$) of the column ($a=H_0/R_0$). We have performed simulations using 2000 elongated grains with length/width ratios up to 5, varying the value of the initial aspect ratio to characterize different flow regimes and the final deposit, and compare with the monodisperse case. Preliminary results indicate that the grain geometry has a significant influence on the collapse of the column.   

Axisymmetric Granular Collapse: a Transient 3D flow Test of Viscoplasticity

The collapse of a stationary cylinder of granular material onto a horizontal plan is a deceptively simple experiment rich in flow behaviour. Using 3-dimensional soft particle simulations, we reproduce the observed scaling laws for the maximum final runout and height of the deposit as a function of the initial aspect ratio. The flow simulations of this unsteady, largely axisymmetric flow are then used to confront a recently-introduced visco-plastic continuum theory (Jop, Forterre \& Pouliquen, {\em Nature}, {\bf 441},727,2006) which has seen some success modelling steady, unidirectional flows.   

Experimental measurements of the collapse of a 2D granular gas under gravity

We experimentally measure the decay of a quasi-2D granular gas under gravity. A granular gas is created by vibro- fluidization, after which the energy input is halted, and the time-dependent statistical properties of the decaying gas are measured with video particle tracking. There are two distinct cooling stages separated by a high temperature settling shock. In the final stage, the temperature of a fluid packet decreases as a power law $T \propto (t_c-t)^\alpha$ just before the system collapses to a static state. The measured value of $\alpha$ ranges from 3.3 to 6.1 depending on the height, significantly higher than the exponent of 2 found in theoretical work on this problem [Phys Rev. E 73, 61305 (2006)]. We also address the question of whether the collapse occurs simultaneously at different heights in the system.   

Three dimensional particle rearrangements during oscillatory flow in a split bottom geometry

We carry out three dimensional imaging of the positions and rearrangements of all particles during slow shear flow of granular matter in a split bottom shear cell geometry. The aim is to gain insights into dense granular flows at the level of individual particle displacements. To image particle motion in three dimensions plastic spheres are used that are immersed in index matching fluid that is fluorescently dyed. This allows for imaging of cross sections with a laser sheet and sensitive camera. Scanning the laser sheet generates a 3D image, from which we reconstruct the position of all particles in a 3D volume. We find that the interior of this fluid immersed material flows in a similar way as dry materials. Our focus is on reversible vs irreversible deformations in granular flows. Reversing the shear direction leads to a flow profile that does not exactly mirror the flow profile before reversal, indicating irreversible deformations in the shear zone. Following the motion of individual particles through at least 10 oscillations shows that the particles far from the shearband return to their original position, but particles in the shear band rearrange. Their mean squared displacement increases subdiffusively with the number of oscillations.   

Session LN: Micro Fluids V

Directional Liquid Spreading on Asymmetric Nanostructured Surfaces

We investigated the ability to manipulate the directionality of liquid spreading by using asymmetric nanostructured surfaces. The nanostructures were composed of silicon pillars with diameters of 250 nm with one side coated with a gold film of thicknesses ranging from 250 nm to 400 nm. Due to the thermal expansion mismatch of the materials, the pillars deflected to angles ranging from 5 to 15 degrees, where the deflection angle was dependent on the thickness of the gold layer. We demonstrated that such asymmetrical structures allow the advancing side of the droplet to spread, while pinning the receding side of the droplet. Detailed experiments were performed to characterize the effect of material properties and nanostructure deflection angle on spreading dynamics. The surface tension of the liquid was also varied to examine the effect on spreading velocity. To interpret the data, we developed a model using an energy minimization approach, which accounted for both the effects of material properties and geometry. This work provides insight into designing asymmetric structures for controlling microfluidic systems.   

Pulsatile flow transport in microscale cavities

Critical to the impact of microfluidics is the ability to transport fluids and biomolecules effectively, particularly at the size scales involved. In this context a bio-inspired pumping mechanism, the valveless impedance pump, was explored for applications in microfluidics ranging from micro total analysis systems to microchannel cooling with the aim of using the pulsatile flow output of the pump to augment transport at low Reynolds numbers. Micro PIV was used to study the affect of both steady and pulsatile flows on transport in microscale rectangular cavities. Ventilation of the cavity contents was examined in terms of the residence time or average time a particle remains in the cavity region. Empirical velocity fields were analyzed using Lagrangian Coherent Structures to determine the impact of unsteadiness on time dependent boundaries to fluid transport present in the flow. Experimental results show that there are both frequencies which are beneficial and detrimental to cavity ventilation as well as certain frequencies which more evenly distribute particles originating in the cavity throughout the freestream.   

Three-dimensional transport of an optically induced electrothermal microvortex

A novel, 3D microfluidic instability is induced from intense laser irradiation applied to a fluid sample contained within a parallel-plate electrode microfluidic chamber. Particles follow the streamlines of this typically toroidal vortex, traveling into and out of focus, which can be visualized with the periodically-varying diffraction ring patterns. These microfluidic vortices assist particle manipulation schemes (e.g. concentration, separation, patterning) as well as show promise as microfluidic mixers. The three-dimensional structure of these vortices is explored using a diffraction-based extension of micron resolution particle image velocimetry ($\mu $PIV) in which the radius of the outermost circle in the diffraction pattern is employed as a metric for the out-of-plane position of the tracer.   

Generating double emulsions W/O/W in a PDMS system by controlling locally the wetting properties of the channel

In microfluidic systems, it has been shown that wetting properties of the wall of the microchannel are of crucial importance for the generation of emulsions [1]: to generate an emulsion in a fluid, the continuous phase must wet the walls of the channel better than the dispersed phase. In the particular case of alternate double emulsions (water in oil in water), it is necessary to pattern the wetting properties of the channel. In this paper, we present preliminary works on the control of wetting properties on PDMS microchannels for the generation of double emulsion. The method we have chosen is inspired by the works of Allbritton [2] and Kumacheva [3] by UV-grafting a hydrophilic polymer onto the surface inside the microchannel. Once the channels are grafted, it is possible to obtain alternate double emulsions. We will present the objects obtained with such microchannels and will focus on their structures and on their stabilities. [1]$^{ }$Dreyfus R., Tabeling P., Willaime H., \textit{Physical Review Letters}, \textbf{2003}, 90(14). [2] Hu S., Ren X., Bachman M., Sims C., Li G.P., Allbritton N. \textit{Anal. Chem}. \textbf{2004, }76, 1865-1870 [3] Seo M., Paquet C., Nie Z., Xua S., Kumacheva E. \textit{Soft Matter}, \textbf{2007}, 3, 986--992   

Enzymatic Reactions in Microfluidic Devices

We establish simple scaling laws for enzymatic reactions in microfluidic devices, and we demonstrate that kinetic parameters obtained conventionally using multiple stop-flow experiments may instead be extracted from a single microfluidic experiment. Introduction of an enzyme and substrate species in different arms of a Y-shaped channel allows the two species to diffuse across the parallel streamlines and to begin reacting. Measurements of the product concentration versus distance down the channel provide information about the kinetics of the reaction. In the limit where the enzyme is much larger (and thus less diffusive) than the substrate, we show that near the entrance the total amount of product ($P$) formed varies as a power law in the distance $x$ down the channel. For reactions that follow standard Michaelis-Menten kinetics, the power law takes the form $P\sim(V_{max}/K_m) x^{5/2}$, where $V_{max}$ and $K_m$ are the maximum reaction rate and Michaelis constant respectively. If a large excess of substrate is used, then $K_m$ is identified by measuring $V_{max}$ far downstream where the different species are completely mixed by diffusion. Numerical simulations and experiments using the bioluminescent reaction between luciferase and ATP as a model system are both shown to accord with the model. We discuss the implications for significant savings in the amount of time and enzyme required for determination of kinetic parameters.   

AC Electrowetting and nanodrop ejection on Conducting Parallel Electrodes

The variation of contact angle for a drop of size $a$ on conducting parallel electrodes is shown via goniometry to be a strong function of the frequency of an applied electric field. While the contact line demonstrates the usual DC electrowetting behavior at low frequencies, no electrowetting was observed at frequencies higher than $\omega _c \sim \frac{D}{\lambda a}$, corresponding to the inverse \textit{RC} time scale for electrode screening. Below this screening frequency, the electric field is focused towards the contact line and leads to nanodrop ejection at a threshold voltage that is frequency dependent. Because of electrode screening, this threshold voltage for nanodrop ejection corresponds to a unique threshold electric field, which is captured with an asymptotic analysis.   

Simulation of gas and water management strategies in PEM fuel cells for UAV power

Proton exchange membrane fuel cells (PEMFC) a involve a number of complex fluid phenomena that are not well understood. The focus of this research is to design a fuel cell that addresses the issues of gas and water management for the power requirements for an Unmanned Arial Vehicle (UAV). Often in conventional stack design, PEM fuel cells are connected electrically in series to create the desired voltage and feed from a common fuel or oxidant stream. This method of fueling, often leads to an uneven distribution of fluid within the stack, causing issues such as cell flooding, dehydration of membrane and inevitably poor fuel cell performance. Generally, fuel cell designers and developers incorporate higher stoichiometric gas flow rates and use flow field designs with high pressure drops in order to counter this phenomenon, ensuring even gas distribution. This method, although effective for water removal, leads to added cost and higher levels of wasted fuel. Using a simulation based approach we demonstrate the feasibility and effectiveness of an individual fuel and oxidant flow distribution, integrated with an individual sequential exhaust technique for a 6-8 cell stack which outputs 300-500 Watts of power. Using varied exhaust configurations the most optimal active gas management strategy will be outlined and recommended to give the best stack performance.   

Inducing Rapid Fluid Flows In Microchannels with Surface Wave Vibrations

The application of MHz-order traveling wave vibrations along a microchannel cut into a piezoelectric substrate results in rapid fluid flows along the channel in the direction of the vibration propagation, up to 2~cm/s in a 50$\times$100~$\mu$m rectangular channel in our device, much faster than other methods known to the authors. The vibration energy carried along the sides and bottom of the channel is diffracted into the channel, imparting momentum to the fluid through streaming. Given the intended application of most microfluidic devices, the fluid would reasonably be expected to carry particles, and introducing micro and nanoparticles into the flow exposes transitions to chaotic behavior, particle collection, and rapid vortex formation and shedding ideal for mixing. We show experimentally and numerically what conditions are necessary for these behaviours, and explain other peculiarities of the chosen system, such as particles traveling upstream from induced forces applied via standing waves formed across the channel during mixing, and transitions between steady and chaotic flow depending on the intensity of the traveling wave vibrations.   

Transmitting High Power RF Vibration via Fluid Couplants into Superstrates for Microfluidic Actuation

Surface acoustic wave (SAW) devices provide acoustic radiation to effectively transport fluids and particles within them for applications in microfluidics, yet require the use of piezoelectric substrates with fabrication chemistry incompatible with industry standard silicon and polymer MEMS materials. Here we couple leaky SAW acoustic radiation transmitted along a lithium niobate-based device through a fluid coupling into a thin glass plate. Though simple application of Snell's law would suggest propagation of the acoustic radiation from the couplant into the glass plate is impossible, we demonstrate the radiation's propagation as a Lamb wave to the top surface of the glass plate with sufficient power to transport small fluid droplets at up to 10~mm/s. Further, we illustrate why this occurs with numerical analysis and experimental measurement of the acoustic radiation. This enables the use of standard processing techniques to fabricate an inexpensive and disposable microfluidics device together with the power transmission capabilities of SAW devices with an easily renewable coupling.   

Vibration Induced Microfluidic Atomization

We demonstrate rapid generation of micron aerosol droplets in a microfluidic device in which a fluid drop is exposed to surface vibration as it sits atop a piezoelectric substrate. Little, however, is understood about the processes by which these droplets form due to the complex hydrodynamic processes that occur across widely varying length and time scales. Through experiments, scaling theory and numerical modelling, we elucidate the interfacial destabilization mechanisms that lead to droplet formation. Droplets form due to the axisymmetric break-up of cylindrical liquid jets ejected as a consequence of interfacial destabilization. Their 10 $\mu$m size correlates with the jet radius and the instability wavelength, both determined from a viscous-capillary dominant force balance and confirmed through a numerical solution. With the exception of drops that spread into thin films with thicknesses on the order of the boundary layer dimension, the free surface is always observed to vibrate at the capillary-viscous resonance frequency despite the surface vibration frequency being several orders larger. This is contrary to common assumptions used in deriving subharmonic models resulting in a Mathieu equation, which has commonly led to spurious predictions in the droplet size.   

Session LP: Multiphase Flows V

Theoretical and numerical study of air layer drag reduction in two-phase Couette-Poiseuille flow

The objective of the present study is to predict and understand the air layer drag reduction (ALDR) phenomenon. Recent experiments (Elbing et al. 2008) have shown net drag reductions if air is injected beyond a critical rate next to the wall. The analysis is performed on a two-phase Couette-Poiseuille flow configuration, which mimics the far downstream region of boundary layer flow on a flat plate. Both theoretical and numerical approaches are employed to investigate the stability and mechanisms of ALDR. The linear stability of air-liquid interface is investigated by solving the Orr-Sommerfeld equations. From the stability analysis, the stability of the interface is reduced as the liquid free-stream velocity, Froude number and velocity gradients at the interface are increased, while the stability is enhanced as the gas flow rate and surface tension are increased. The Critical gas flow rates from stability theory are compared with experimental results, showing good agreement. Direct numerical simulations with a Refiend Level Set Grid technique has been performed to investigate the evolution of the interface, the turbulence interaction and nonlinear mechanisms of ALDR. It is observed that the Weber number has significant impact on the characteristics of the interface development.   

Time-resolved simulations and experiments of liquid jet break-up

High-speed, high-resolution experimental visualization of the break-up of a liquid jet by a gaseous cross-flow has recently become possible due to advances in video camera technology. These visualizations can now be contrasted to high fidelity CFD simulations which are also just becoming possible due to continuing growth of computational capabilities. Such a contrast is expected to go beyond traditional comparisons of time-averaged quantities and focuses on dynamics. For example, comparisons of the characteristic break-up frequency and of the spatial instantaneous features of the jet may serve as validation of the computational model and to yield insight into the physics of the dynamic interplay between the disturbances induced by the injection device and Kelvin-Helmholtz / Rayleigh-Taylor instabilities at the interface. A state-of-the-art second-order coupled Level Set and Volume Of Fluid method (CLSVOF) that can capture liquid-gas interface dynamics is used for the study. High-speed videos of non-turbulent liquid injection in laminar crossflow are used to validate the time- and grid-converged capability of the code to capture upwind wave structures caused by the centrifugal acceleration of the deflected liquid. The extension to increasing air crossflow is also discussed with focus on the column break-up mechanism.   

Large-eddy simulation of particle-laden flow over a backward-facing step using a spectral multidomain method

We present an investigation into the particle-laden flow in a dump-combustor configuration. An accurate prediction of particle dispersion within the combustors is necessary for improved design of spray combustion. The instantaneous local particle concentration and turbulent mixing provide insights into the physio-chemical processes that would be encountered in a reacting scenario. The principal difficulty in prediction of particle transport in the dilute flow regime, lies in the accurate description of the underlying complex, turbulent gas flow field featuring reattaching shear layers. Here, we present large-eddy simulations (LESs) of a particle-laden flow over an unconfined and confined backward-facing step at Reynolds numbers of 5000 and 28,000, respectively, using a spectral multidomain LES methodology. The LES captures the carrier flow accurately, while being computationally affordable. One-way coupled equations are considered and particles with different Stokes numbers are studied. The inlet turbulence is modeled using a novel stochastic model that reproduces the second order moments of the fully developed flow upstream of the step. The effects of the turbulent recirculating flow behind the step on particle dispersion are investigated in detail.   

Immersed Boundary and VOF Coupling Method for Bubble-Particle Interaction Problems

A new approach for the direct numerical simulation of three-phase flows is described. The method permits the simulation of the flow induced by a large population of bubbles and particles in a gas-liquid-solid system. Implementation of moving rigid surfaces is based on an immersed boundary method (IBM) of the body-force type, also developed by the present authors. In this method, the inter-phase momentum exchange is calculated by the distributed interaction force field shared by both the Eulerian (fluid) and Lagrangian (particles) frameworks. The gas-liquid interfaces are captured by the volume of fluid (VOF) method including surface tension. To assess its validity, the present method is applied to the piercing of the free surface of a liquid by a rising cylinder. Further applicability of the method is demonstrated in a 3-D situation, in which a rising bubble interacts with many settling particles.   

Experimental and numerical investigation of multiphase flow in disordered media

We present laboratory scale experiments and network simulations to investigate the influence of capillary, gravitational and viscous forces on multiphase flow in disordered microscopic media. Two-dimensional experiments, which are performed in a vertical glass bead pack to understand microscopic behavior, demonstrate the existence of small scale instability that is analyzed with the theory of invasion percolation. Numerical simulations based on pore networks are carried out to help investigate the possibility of developing effective conservation laws at the macroscopic scale.   

Towards numerical simulation of bubbly flows in complex geometries

We are developing the LES capability for bubbly flows in complex geometries using unstructured grids and an Euler--Lagrangian methodology. Two Lagrangian bubble models are considered:\ (i) the bubbles are treated as a dispersed phase in the carrier fluid, and individual bubbles are point particles governed by an equation for bubble motion and (ii) the force coupling method by \mbox{Maxey$\!$ \textit{et al.}}\ \mbox{[\textit{Fluid Dyn.\ Res.}, \textbf{32} (1997), 143-156]}. The evolution of the bubble radius (assuming spherical bubbles) is governed by the Rayleigh--Plesset equation and integrated using a Runge--Kutta integrator with adaptive time-stepping. The talk will discuss numerical issues and contrast results between the two methodologies. Numerical results ranging from the motion of individual bubbles in channels and around bodies to drag reduction by bubbles in turbulent channel flow will be presented.   

Diffuse-interface modeling of phase segregation in van der Waals fluids

We simulate phase separation in a van der Waals fluid that is deeply quenched into the unstable range of its phase diagram. Our theoretical approach follows the diffuse-interface model, where convection induced by phase change is accounted for via a Korteweg force, expressing the tendency of the demixing system to minimize its free energy. Spinodal decomposition patterns for critical and off-critical van der Waals fluids are studied numerically, revealing the scaling laws of the typical length scale and composition of single-phase microdomains, together with their dependence on the Reynolds number. Unlike phase separation of viscous binary mixtures, here local equilibrium is reached almost immediately after single-phase domains start to form. In addition, as predicted by scaling laws, such domains grow in time like $t^{2/3}$. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon. For a binary mixture of van der Waals fluids, we show simulations of Marangoni migration during phase separation in a temperature gradient. Our results reproduce the large-scale unidirectional convection observed in recent experiments.   

The Effect of Water Compressibility on a Rigid Body Movement in Two Phase Flow

The motion of a rigid body in a tube full of water-filled, initiated by a sudden release of highly pressurized air is simulated presuming the flow field as a two dimensional one. The effects of water compressibility on the body movement are investigated, comparing results based on the Fluent VOF model where water is treated as an incompressible medium with those from the presently developed VOF scheme. The present model considers compressibility of both air and water. The Fluent results show that the body moves farther and at higher speeds than the present ones. As time proceeds, the relative difference of speed and displacement between the two results drops substantially, after acoustic waves in water traverse and return the full length of the tube several times. To estimate instantaneous accelerations, however, requires implementation of the water compressibility effect as discrepancies between them do not decrease even after several pressure wave cycles. This work was supported by a research fund granted from Agency for Defense Development, South Korea.   

Two Phase Compressible Flow Fields in One Dimensional and Eulerian Grid Framework

Numerical investigation for two phase compressible flow fields of air-water in one dimensional tube are performed in the fixed Eulerian grid framework. Using an equation of states of Tait's type for a multiphase cell, the two phase compressible flow is modeled as equivalent single phase which is discretized using the Roe`s approximate Riemann solver, while the phase interface is captured via volume fractions of each phase. The most common problem found in the computational approaches in compressible multiphase flow is occurrence of the pressure oscillation at the phase interface. In order to suppress that phenomenon, tried are two approaches; a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The results show that the direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. This work was supported by a research fund granted from Agency for Defense Development, South Korea   

A moving mesh interface tracking method for multiphase flows with topological changes

A moving mesh interface tracking (MMIT) method with local mesh adaptations on tetrahedral elements was developed to simulate incompressible, immiscible multiphase flows with large deformation and topological changes. The interface is represented by triangle elements, and moves with the fluid velocity. The boundary conditions across the interface are implemented directly without any smoothing of the fluids' properties as the interface is zero thickness. Mesh adaptations including smoothing, coarsening and refining are applied locally to achieve computing efficiency as well as to maintain good mesh quality. In order to handle the challenges such as interface breakup and merging, mesh separation and mesh combination are employed. These two schemes are based on the conversion of elements in one liquid phase to anther fluid by changing the fluid properties of the cells in the separation or combination region. The newly created interface is usually ragged, so a local projection method is applied to smooth the interface. Simulations of droplet oscillations and droplet-pair collisions show that the method is accurate in simulating two-phase flow, and that the method has the potential to perform detailed investigations of liquid particles breakup and coalescence.   

Session LQ: Reacting Flows III: Flames and Modeling

Autoignition of hydrogen and air using direct numerical simulation

Direct numerical simulation (DNS) is used to study to auto--ignition in laminar vortex rings and turbulent diffusion flames. A novel, all--Mach number algorithm developed by {Doom et al} ({\it J. Comput. Phys.} 2007) is used. The chemical mechanism is a nine species, nineteen reaction mechanism for $H_2$ and Air from Mueller at el ({\it Int. J. Chem. Kinet.} 1999). The vortex ring simulations inject diluted $H_2$ at ambient temperature into hot air, and study the effects of stroke ratio, air to fuel ratio and Lewis number. At smaller stroke ratios, ignition occurs in the wake of the vortex ring and propagates into the vortex core. At larger stroke ratios, ignition occurs along the edges of the trailing column before propagating towards the vortex core. The turbulent diffusion flame simulations are three--dimensional and consider the interaction of initially isotropic turbulence with an unstrained diffusion flame. The simulations examine the nature of distinct ignition kernels, the relative roles of chemical reactions, and the relation between the observed behavior and laminar flames and the perfectly stirred reactor problem. These results will be discussed.   

Influence of Standing Acoustic Waves on Combustion of Alternative Fuels

The present experimental study focuses on exposure of single burning fuel droplets to external acoustical excitation created in a cylindrical waveguide bounded by two loudspeakers. This configuration creates a relatively symmetric acoustic field whereby standing waves may be created, forming a pressure node (PN) or antinode (PAN) within the waveguide. A range of alternative liquid fuels is considered in these experiments, including ethanol, methanol, white gasoline, JP-8, and blends of JP-8 and liquid synthetic fuel. Droplet burning rates, flame characteristics, and their dependence on the position of the droplet relative to the PN and PAN are quantified. In some cases, large scale acoustic forcing is observed to cause flame deflection so strong that the effective acoustic radiation force appears to approach the magnitude of the buoyant force acting on the flames. Flame orientation is observed to change abruptly as the droplet position is moved from one side to the other relative to the PN or PAN, consistent with theory,\footnote{Tanabe, et al., {\bf Proc. Comb. Inst.} 30, p. 1957-1964, 2005} although for very large amplitude acoustic forcing, the magnitude of the acoustic acceleration can exceed theoretical predictions. Variations in burning rates for a range of fuels and excitation conditions relevant to engine systems are quantified.   

Constructing Slow Invariant Manifolds for Reactive Systems with Detailed Kinetics

Rational reduction of reactive systems becomes possible when their Slow Invariant Manifolds (SIMs) are identified. In this work, a robust method of constructing the one-dimensional SIMs for unsteady spatially homogeneous reactive systems is presented. The method is based on global analysis of the composition phase space of the reactive system, where all critical points, finite and infinite, are identified using a projective space technique. Then by connecting these equilibria via trajectories, the SIM can be characterized. Employing the projective space technique offers the possibility to construct SIMs for detailed kinetic systems ({\em e.g.} $H_2$- $Air$). Moreover, the relation between reactive systems dynamics and the thermodynamics is examined, and it is shown that classical thermodynamics potentials cannot identify the SIM.   

Pinning of reaction fronts by moving vortices

We present experimental and numerical studies of the effects of moving vortices on the propagation of reaction fronts. The front is produced by the excitable Belousov-Zhabotinsky chemical reaction, and the flow is forced with a magnetohydrodynamic technique. An individual vortex or vortex pair moving in the same direction as a front often pins and drags the front, with a maximum pinning speed that depends on the strength of the vortex. In an extended system, the moving vortex leaves a wake-like structure that dramatically affects the overall front. Multiple pinning vortices leave a pattern of wakes that combine to form more complicated front structures. We extend these experiments to random patterns of vortices which produce complicated pinned fronts whose detailed structure depends on the speed of the vortices relative to the background fluid. The experiments are complemented by numerical simulations that simplifies the large-scale behavior by modelling moving vortices as pinning centers.   

The Effects of Time-Periodic Shear on a Diffusion Flame Anchored to a Model Propellant

Propellants of solid rocket motors are subject to intense time-dependent shear flows and the response of the combustion field to these flows is of fundamental interest. Erosive burning (EB), the enhanced regression rate that can arise due to these flows, affects the performance of the solid rocket motor: the specific-impulse history. It is generally agreed that EB results from an increased heat transfer to the surface. The geometry is that of two quarter-planes of ammonium perchlorate (AP) and binder (or a blend of AP/binder). Three step kinetics is considered: AP decomposition and two diffusion flames, one between the virgin AP gases and binder and one between AP decomposed gases and binder. Gas and solid phases are coupled and temperature along the surface as well as the burn rate is solved for. We present an estimation of the shear parameters as a function of the motor size using a 2D planar periodic rocket (PPR) analysis without resorting to fully time-dependent three-dimensional turbulent simulations. These parameters are then used to study the change in the heat flux to the surface and the burn rate. It is shown that the burn rate is increased by more than two folds for larger amplitudes and frequencies.   

Flame propagation in dusty gases

The combustion of finely atomized dust particles is of great importance to many practical technologies. While the study of flame propagation through gaseous fuel-air mixtures is relatively well developed, there currently exists a lack of fundamental understanding on the mechanisms that govern flame propagation through dust clouds. Unlike homogeneous gas flames, the study of metal particle combustion is highly complex, involving chemical and physical processes occurring in multiple phases. The mathematical description requires particular importance to be placed on the processes occurring in the condensed phase, for they present novel challenges in dust combustion modeling and ultimately provide its most distinguishing characteristics. Typical reaction zones are confined to a thin region of space and necessitate the use of perturbation methods with distinguished limits in order to capture the essential behavior of the system. Through matched asymptotic expansions we are able to arrive at an expression for the speed of the propagating flame front in terms of important combustion parameters such as mixture strength, particle loading, and particle size.   

The structure of partially-premixed methane/air flames under varying premixing

The present work examines the spatial and scalar structure of laminar, partially premixed methane/air flames with the objective of developing flamelet mappings that capture the effect of varying premixture strength (air addition in fuel.) Experimental databases containing full thermochemistry measurements within laminar axisymmetric flames were obtained at Sandia National Laboratories, and the measurements of all major species and temperature are compared to opposed-jet one-dimensional flow simulation using Cantera and the full chemical kinetic mechanism of GRI 3.0. Particular emphasis is placed on the scalar structure of the laminar flames, and the formation of flamelet mappings that capture all of the salient features of thermochemistry in a conserved scalar representation. Three different premixture strengths were examined in detail: equivalence ratios of 1.8, 2.2, and 3.17 resulted in clear differences in the flame scalar structure, particularly in the position of the rich premixed flame zone and the attendant levels of major and intermediate species (carbon monoxide and hydrogen).   

Spectral closure for the probability density function of reactive scalars in isotropic turbulence

We present a spectral closure for the joint composition probability density function (PDF) for multiple scalars undergoing isothermal chemical reactions. The formulation, based on the eddy damped quasi-normal Markovian (EDQNM) theory, accounts for macroscopic mixing and scalar dissipation separately and allows for differential diffusion of reactant and/or product species due to differences in their molecular diffusivities. The EDQNM theory has been reformulated into a stochastic differential equation for the particle concentrations in a Monte Carlo scheme. We present results for non-premixed isotropic scalars and one-dimensional mixing without and with differential diffusion. Results are compared with direct numerical simulations (DNS). The model captures well the competing effects of mixing, chemical reaction and differential diffusion.   

Turbulence-flame interactions in type Ia supernovae

The small-scale dynamics of nuclear flames in the supernova environment are examined using high-resolution three-dimensional simulations in which the details of the flame structure are fully resolved. The range of densities examined, $1$ to $8 \times 10^7$~g~cm$^{-3}$, spans the transition from the laminar flamelet regime to the distributed burning regime, where small-scale turbulence disrupts the flame. The use of a low Mach number algorithm facilitates the accurate resolution of the thermal structure of the flame and the inviscid turbulent kinetic energy cascade, while implicitly incorporating kinetic energy dissipation at the grid-scale cutoff. For an assumed background of isotropic Kolmogorov turbulence with an energy characteristic of a type Ia supernova, we find a transition density between $1$ and $3 \times 10^7$~g~cm$^{-3}$, where the nature of the burning changes qualitatively. This transition from flamelet to distributed burning reveals important consequences for turbulent flame models.   

Front propagation in vortex-dominated flows

We present experiments that explore how the propagation of a reaction front is affected by a two-dimensional flow dominated by vortices. The reaction is the excitable Belousov-Zhabotinsky chemical reaction. The flow is driven by the interaction between an electrical current passing through the fluid and a spatially-varying magnetic field produced by an array of magnets below the fluid. For some of the experiments, the forcing is strong enough to produce a weakly turbulent flow. Measurements are made both of the enhanced diffusion coefficient $D^*$ describing transport in the flow and of the propagation speed $v$ of a reaction front in the same flow. Scaling of $v$ versus $D^*$ is compared with that for the standard Fisher-Kolmogorov-Petrovsky-Piskunov prediction $v \sim \sqrt{D}$ (with $D$ as the molecular diffusion coefficient) for the reaction-diffusion limit with no fluid advection. We also study the effects of superdiffusive transport and L\'evy flights on front propagation in a time-dependent vortex array with wavy jet regions.   

Session LR: General Fluid Mechanics: Theory

Velocity fluctuations and energy amplification in laminar fluid flows

We present a systematic procedure for evaluating the intrinsic velocity fluctuations and the resulting intrinsic energy amplification that are always present in laminar fluid flows. For this purpose we formulate a stochastic Orr-Sommerfeld equation and a stochastic Squire equation by applying a fluctuation-dissipation theorem for the random part of the dissipative stresses. From the solution of the stochastic Orr- Sommerfeld and Squire equations the intrinsic energy amplification can be deduced. As an illustration of the procedure we present an explicit solution for the case of planar Couette flow. We first solve the fluctuating hydrodynamics equations in the bulk, obtaining an exact representation of the spatial spectrum of the velocity fluctuations valid for large wave numbers. The resulting energy amplification is proportional to $Re^{3/2}$. Next, we show how to a good approximation confinement can be incorporated by a simple Galerkin projection technique. The effect of the boundary conditions is to reduce the energy amplification to a logarithmic dependence on $Re$. We shall also indicate how an exact solution for the case of confined geometries can be obtained by an expansion into a set of hydrodynamic modes, conveniently expressed in terms of Airy functions.   

Nonlinear Model of Turbulent Dynamo and Assimilation of Sunspot Data

We investigate a non-linear dynamical model to describe the cyclic behavior of magnetic fields on the Sun. The model is derived by applying a low-mode approximation to the mean-field turbulent dynamo theory and taking into account variations of magnetic helicity. We show that the model reproduces the observed behavior of the Sun's global magnetic field: the periodic polarity reversals, migration towards the equator, and the relationship between the growth rate and the strength of the 11-year sunspot cycles. In addition, the model has chaotic regimes, which may be important for understanding the long-term behavior of the solar cycles. Since the properties of the solar dynamo, such as turbulent diffusion and helicity, are unknown, we apply data assimilation methods for obtaining the best estimate of the true state of the system and also for predicting the next cycle. In particular, we used the Ensemble Kalman Filter and recent modifications, to assimilate the sunspot data available for 1755-2008 into the model. We compare the assimilation results and discuss the predictions of the next sunspot cycle.   

Entrainment Phenomena in Potential Flow: Brachistochrones and Finite-Time Corrections to Darwin's Drift Volume

For a body moving uniformly in an ideal fluid there exists a region in which particles are swept in the same direction as the motion of the body, called the drift region, as well as a region in which particles are forced in the opposite direction as that of the body, called the reflux region. In Darwin's Theorem, the drift volume is defined as the volume swept out by particles originating on a plane perpendicular to the motion of the body, as the body moves from an infinite distance upstream of the plane to an infinite distance downstream of the plane. Here, we present finite-time corrections to Darwin's calculation of the drift volume for a sphere, which extend the previously obtained semi-infinite correction of Eames, Belcher, and Hunt (1994). Additionally, we solve the problem of finding the particle who minimizes its time of flight for uniform flow past a sphere. The path of this particle who minimizes flight time is termed the brachistochrone path, and a connection is drawn to the geometry of the reflux region.   

Float height and quasi-steady spin-down of a rotating disk

Numerical integrations of the self-similar equations for steady fluid motion between parallel infinite disks are reported for the case where the upper impermeable disk rotates and the lower stationary disk has uniform transpiration. The numerics are facilitated by a high-Reynolds number asymptotic analysis. The results are applied to model the float height of the steadily spinning disk under gravity when the disk separation is small. We find that the disk will touch down when it has sufficiently high angular rotation. Boundaries separating regimes of radial outflow from counter-flow and disk touch down are determined over a range of blowing Reynolds numbers $R$ and swirl parameters $S$. In certain regimes of parameter space and disk geometry the results provide a quasi-steady estimate for the spin-down dymamics of a disk in free rotation over an air- bearing table. Experiments are under way to test the validity of this quasi-steady approximation.   

Flow between concentric cylinders driven by an electromagnetic force

We study a two-dimensional magnetohydrodynamic (MHD) laminar flow of a viscous electrically conducting fluid between concentric cylinders. The flow is produced by an electromagnetic force due to the interaction of a uniform axial magnetic field and a radial electrical current. We analyzed two situations, namely, when the electric current is produced by a steady potential difference between the walls of the cylinders and when the potential difference oscillates in time. The magnetic field induced by the fluid motion is assumed to be negligible compared to the applied magnetic field. In both cases, the flow is described in terms of closed analytical expressions. A parametric study covering a range of Hartmann numbers is conducted and it is found that for a given a electrical potential difference, the fluid velocity as a function of the Hartmann number has a local maximum.   

The Hamiltonian description of incompressible fluid ellipsoids

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler's equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie-Poisson form.   

Taylor dispersion and the optimization of residential geothermal heating systems

Residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. These systems consist of tubing (2 cm radius, 1 km in length) buried below the ground surface through which a coolant flows. Tube length has a direct correlation to installation cost. The temperature of this fluid rises as it flows through the tubing, and the energy from this temperature difference is utilized to heat the residence. As a first model, we consider a single tube of fluid encased in an infinite medium of soil, with the goal to find the minimum length over which temperature variations occur. Through lubrication theory, we derive an evolution equation for the local soil temperature near the tubing. We find that Taylor dispersion of heat in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. Next, matched asymptotics is used to incorporate far-field temperature variations. Comparison of our model with experiment is presented.   

Theoretical Analysis of the Two-Scale Direct-Interaction Approximation for the Turbulent Passive-Scalar Field Including Molecular Viscosity and Diffusion Effects

A fluctuating field of a passive scalar in turbulent flow is theoretically investigated by means of a two-scale direct-interaction approximation theory including the effects of a molecular viscosity and diffusion. Solving the fluctuating field in a perturbational manner, we get the energy and scalar intensity spectra and the eddy-viscosity representation for the Reynolds stress and scalar flux in the case that the Prandtl number is around 1. The derived spectrum of the passive scalar intensity is the Obukhov-Corrsin spectrum in the inertial subrange and is proportional to the -3 power law in the dissipation subrange. Applying the Pade approximation to the obtained spectrum expressions, the present spectra are consistent with the Pao's empirical ones. The new eddy-viscosity representations for the Reynolds stress and scalar flux include the molecular viscosity and diffusion effects through the turburent Reynolds number and Prandtl one.   

Session LS: Convection I

Convective Instabilities of Binary Mixtures in Annular Thermogravitational Columns

A theoretical and computational study of Soret separation of a binary mixture contained in a differentially heated infinite vertical annulus is presented. We first calculate the basic steady one-dimensional flow taking into account the vertical concentration gradient caused by thermodiffusion. Unstable (stable) stratification is induced at positive (negative) separation ratios. Linear stability of this basic state is performed and the critical Rayleigh number, wave number, frequency, and vertical concentration gradients are determined as functions of the separation ratio, Lewis and Parndtl numbers. It is shown that the preferred instability is axisymmetric when the induced vertical stratification is stable while it is azimuthal with unstable vertical stratification. Supercritical nonlinear computations are in agreement with linear theory and available experiments. Stability restrictions on the operation of the thermogravitational column will be discussed.   

Two Dimensional Unsteady Convection in Pressure-Driven Nitrogen Flow in Long Microchannels with Uniform Heat Flux Input

The transient features of pressure-driven Nitrogen flows in long microchannels under uniform heat flux input conditions are numerically studied. The two-dimensional momentum and energy equations are solved, where variable properties, rarefaction effects, including velocity slip, thermal creep, and temperature jump, as well as compressibility and viscous dissipation effects, are all taken into account. This paper focuses on two conditions: a sudden heat flux change at the channel wall and a sudden inlet pressure change. The thermal and fluid dynamics after these two changes are described and discussed in detail. The approach to steady-state conditions and the overall transient response are investigated. It is found that the overall transient response for the case with a sudden increase in the heat flux input is slower than that for the case with a sudden decrease in the heat flux input. The transient response for the case with a sudden increase in the inlet pressure is much faster than that for the case with sudden decrease in the inlet pressure. Based on the results obtained earlier, the difference in overall transient response is mainly caused by the energy taken up by the pressure work. Other physical results are obtained and discussed.   

A study of the effect of surface conditions on free-surface evaporative convection

An experimental study is presented of free-surface evaporative convection in both the presence and absence of a surfactant monolayer. The transfer of heat and the evaporation rate are quantified by parameterizing the Nusselt and Sherwood numbers in terms of the Rayleigh number. The goal of this study is to determine how these $Nu-Ra$ and $Sh-Ra$ relationships change when the hydrodynamic boundary condition is changed at the free surface. Specifically, two cases are presented: 1) a surface covered with a surfactant monolayer having a finite elasticity, and 2) a clean surface having zero elasticity. The resulting $Nu-Ra$ parameterization is also compared to investigations of the classical Rayleigh-B\'{e}nard experiment where the hydrodynamic boundary condition is of the no-slip type.   

Turbulent Thermal Convection with Polymer Additives

We study the effect of polymers in natural convection and test a new approach for the numerical resolution of the transport of low-diffusion scalars. Our natural convection incompressible flow takes place between two infinite parallel isothermal plates. We present simulations for Rayleigh numbers up to $5\times10^6$ for water alone and water with polymer additives. The behavior of polymer solutions, simulated using viscoelastic models, is analog to that observed in drag-reduced polymer wall flows. The polymers damp vortices (secondary instability, quasi streamwise vortices for wall flows) caused by thermal plumes, resulting in stronger and more coherent convection cells (primary instability, streaks). The overall heat transfer is significantly reduced. For some simulations, we have used a new numerical algorithm, the Adaptive Lagrangian Gradient Transport, to resolve sharp gradients of temperature and components of the polymer stress tensor. The algorithm calculates scalar gradients using a traditional finite-difference Eulerian approach in regions where the method is numerically stable. In the rest of the flow, determined by its local topology, the algorithm reconstructs gradients at computational nodes from particles that transport governing equations for the scalar gradients of interest.   

Pattern formation in anticonvective systems

Two-layer fluid systems with an undeformable interface heated from above in the presence of gravitational forces may show a rather paradox transition from conductive to convective states. This instability was found by {\sc Welander}[1] in 1964 and named anticonvection. Besides the applied temperature gradient various interactions at the interface play an essential role for anticonvection. I.e. this instability depends very sensitive on material parameters. Here we use the Boussinesq-approximation for incompressible fluids and classical boundary conditions of an undeformable interface. Starting from the basic hydrodynamic equations we derive the equations for the perturbed fields of the stationary state. A linear stability analysis for vertically infinitely extended systems can be done analytically. However, vertically bounded systems (in particular for experimental realization) require numerical investigations. We discuss the instability regime, influence of material parameters and show how vertical bounding effects this instability. Finally, numerical simulations of the fully nonlinear system show the resulting patterns for an anticonvective system and reveal velocity and temperature distributions in both fluids. \vspace*{1em} [1] P.Welander, Tellus {\bf 16}, 349 (1964)   

Analysis of Stability of Channel Flow Subject to Distributed Heating

The linear stability of channel flow between two horizontal parallel walls in the presence of distributed wall-heating has been investigated. The case of periodic heating applied at the bottom wall has been considered in details. This heating results in the creation of zones of fluid with alternatively increased and decreased temperature. The mean flow and the linear stability equations have been solved using spectral methods. Two types of instability, i.e., vortex instability and traveling wave instability, have been examined. For the traveling wave instability two and three dimensional oblique waves have been considered. It has been found that from among various possible forms of disturbances the streamwise vortices appear at the lowest value of the Rayleigh number if the flow Reynolds number is sufficiently small, and two-dimensional Tollmien-Schlichting (TS) waves appear first if the flow Reynolds number is sufficiently large. The conditions when the two-dimensional waves dominate are similar to those found in the case of isothermal flow.   

Buoyancy-driven convection around exothermic autocatalytic chemical fronts

Spatiotemporal distributions of heat and mass across chemical fronts propagating in horizontal solutions can initiate buoyancy-driven convection. The goal of our work is to theoretically investigate the dynamics due to the coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows. To do so, we numerically integrate the incompressible Stokes equations coupled through buoyancy terms to conservation equations for the concentration of the reaction product and for the temperature. A solutal and a thermal Rayleigh number measure the coupling between reaction-diffusion processes and buoyancy convection. The asymptotic dynamics in the case of an isothermal front is a steady vortex surrounding, deforming, and accelerating the front (L. Rongy, N. Goyal, E. Meiburg and A. De Wit, J. Chem. Phys. 127, 114710, 2007). We address here the influence of thermal effects on the dynamics of the system. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection, particularly when the solutal and thermal effects are antagonistic, leading to temporal oscillations of the concentration, temperature, and velocity fields in a reference frame moving with the front. The influence of the Lewis number measuring the ratio between thermal and molecular diffusivity is investigated.   

Buoyancy-driven instabilities induced by chemical reactions in vertical porous media

Classical Rayleigh-Taylor or double diffusive instabilities can be triggered by a simple A+B$\rightarrow $C chemical reaction when two miscible solutions each containing one reactant are put in contact in the gravity field. A linear stability analysis of the evolving base state profiles is performed using a quasi-steady state approximation. This allows one to classify the various sources of instabilities as a function of the parameters which are the Rayleigh numbers and the ratio of diffusion coefficients of the chemical species. The resulting nonlinear dynamics due to this chemo-hydrodynamic feedback are then systematically analyzed to highlight how the chemical reaction can trigger or modify the hydrodynamical instabilities. It is also shown to what extent the~resulting buoyancy-driven instabilities enhance the total reaction rate. Finally, related experiments are also performed in a vertical Hele-Shaw cell with an acid-base reaction.   

Experimental investigation on coupling flows between liquid and liquid metal layers

This study aims to clarify coupling of flows between liquid metal and other usual liquids, e.g. water or oil, in fluid dynamical systems. In past studies for two-layer Rayleigh-B\'enard system where the immiscible two liquids are layered, two types of coupling were observed; these are called as ``mechanical coupling'' and ``thermal coupling.'' As a typical character of low \textit{Pr} fluid, large-scale structure in the liquid metal layer has oscillating motion. In this study we investigate ``thermal coupling'' especially how the oscillation of cells in the liquid metal layer propagates to the upper liquid layer and vice versa by changing a ratio of the height of the layers and viscosity of the upper layer fluid. Visualization of the liquid metal motion was conducted by means of ultrasonic velocity profiling, and then the oscillating motion is expressed on the space-time velocity map. PIV measurement of the upper, transparent fluid layer shows the modulation of the convective motion due to the oscillation in the liquid metal layer. Point-wise measurement of temperature at several positions in the fluid layer represents the modulation quantitatively.   

Plume shot noise in convection: evidence of a boundary layer instability consistent with the triggering of the Ultimate regime of convection

A sudden enhancement of the heat transfer for Rayleigh numbers Ra$>$1e12 was reported in a Rayleigh B\'{e}nard cell in 1997 (Chavanne et al. PRL).This observation was interpreted as the occurrence of Kraichnan's ``Ultimate'' regime of convection, which is characterized by turbulent boundary layers. This interpretation has been indirectly supported by the outcome a test experiment, using a cell with corrugated surfaces. A more direct test would consist in probing fluctuations within the boundary layer, but its thinness (order 100 microns) causes instrumentation challenges. To overcome this difficulty, we recorded the shot noise induced by the thermal plumes leaving the bottom plate. We find that the heat transfer enhancement at Ra$\sim $1e12, is accompanied by a significant increase of shot noise. This observation is interpreted as the signature of a boundary layer instability, in agreement with the Ultime regime scenario. [ Gauthier F. and Roche P.-E et al., EPL 83:24005 (2008) ] \\[3pt] In collaboration with Fr\'ed\'eric Gauthier and Philippe-E. Roche, Institut NEEL, CNRS.   

Session LT: Non-Newtonian Flows I

Mesoscopic dynamics of polymer chains in high strain rate extensional flows

The study of high speed aerobreakup of polymeric liquids is obstructed by the lack of standard viscoelastic constitutive laws valid for high strain rate extensional flows. In order to reliably estimate polymer induced elastic stresses in these processes, we perform Brownian dynamics calculations of a bead-spring polymer model at high Deborah numbers. The predictions of our computational chain model match experimental largest relaxation time and elastic stress levels. By kinematically prescribing the solvent flow, we study polymer response in dilute, high strain rate extensional flows typical of aerobreakup experiments clarifying the physical mechanisms of chain stretching and computing transient extensional viscosities. In the context of confined systems, we investigate the dynamical effects of topological chain entanglement.   

A microfluidic study of the rheology, slippage and flow instabilites of wormlike micelles

We characerize by Particle Image Velocimetry the Poiseuille flow semi-dilute solutions of wormlike micelles (a CTAB and sodium nitrate aqueous solution and a CpCl solution) in pressure resistant microchannels. Thanks to the high aspect ratio of our channels, we can measure the local rheology of the solution, independantly from the slippage at the wall, according to a method already validated on non-newtonian polymer solutions. As the pressure driving the flow is increased, the velocity profiles reveal first a newtonian phase, then apparition of a dramatically lower viscosity second phase at the walls, which is the so called shear banding regime. First we deduce the local rheology of the solution from these velocity profiles. This method gives access to the stress versus shear rate relation over a domain unexplored in classical Couette geometries, characterizing more than a decade of deformation rates for the high shear phase. Then we measure the slip length to be below 1.5 microns in these flows. Finally we study the development of an instability at the interface between the two phases, similarly to what has already been found in Couette like geometries.   

Numerical simulations of time-dependent, fully 3-D viscoelastic flows past bluff bodies

With the goal of creating a robust numerical method for simulating three dimensional, time dependent non-Newtonian flows, we have developed an unstructured, finite-volume code to compute a wide variety of viscoelastic flows over a large range of Reynolds ($Re$) and Weissenberg ($Wi$) numbers. Our method is based on the FENE-P constitutive model to describe the flow of dilute polymeric solutions, and an implicit time-stepping technique is utilized that properly maintains boundedness of the polymer stresses and extensions even at high flow strengths. We will present the time-dependent, viscoelastic flow past a circular cylinder at moderate $Re$ ($Re \sim O(100)$). Within this range, regular vortex shedding occurs, and the characteristic frequency of this shedding was found to decrease with increasing fluid elasticity. Furthermore, the coefficients of both friction drag and form drag are reduced with increasing $Wi$, and new qualitative effects have been observed at large polymer lengths where the cylinder drag rises dramatically due to a rapid increase in form drag. Physical mechanisms for this behavior will be proposed and discussed.   

Vertical structures in vibrated wormlike micellar solutions

Vertically vibrated shear thickening particulate suspensions can support a free-standing interfaces oriented parallel to gravity. We find that shear thickening worm-like micellar solutions also support such vertical interfaces. Above a threshold in acceleration, the solution spontaneously accumulates into a labyrinthine pattern characterized by a well-defined vertical edge. The formation of vertical structures is of interest because they are unique to shear-thickening fluids, and they indicate the existence of an unknown stress bearing mechanism.   

A Mixing Transition in a Viscoelastic Fluid

Dynamical behavior in low Reynolds number viscoelastic flows is investigated numerically in the Oldroyd-B model. For low Weissenberg number, flows are ``slaved" to the four-roll mill geometry of the body forcing. For sufficiently large Weissenberg number, such slaved solutions are unstable and under perturbation transit in time to a structurally dissimilar flow state dominated by a single large vortex, rather than four vortices of the four-roll mill state. The transition to this new steady-state also leads to regions of well-mixed fluid, and may be related to a recently discovered transition in cross-channel flows of a viscoelastic fluid.   

Filament break up, drop size and non- Newtonian borate esters in jet flows

Study and analysis of jet flows has found application in such industrial applications as spray coating and inkjet printers. Length-scales and timescales in controlling the dynamics of the thinning and break-up process is found to depend on gravitational forces, surface forces, and mechanical forces shear and extensional forces acting on a fluid. If the gravitational effects are not important, midpoint radius of the viscous filament for Newtonian fluids has been analyzed to depend on the ratio of surface tension to viscosity of the fluid and the process time. The ratio of time to breakup for the visco-capillary and inertio-capillary processes is related to a dimensionless number known as the Ohnesorge\textit{ number }In non-Newtonian and visco-elastic fluids, filament radius is dependent on the ration of relaxation modulus to surface tension and exponentially decays with the ratio of process time to the fluid (polymer) relaxation time. Analogous to Ohnesorge number, time scale of break up, in non-Newtonian and visco-elastic fluids, time scale of break up is Deborah number, the ratio of relaxation time to process time. Using fluids of glycol, polyethylene oxide and borate esters, torsion strain experiments were used to determine viscosity and visco-elastic parameters (relaxation modulus and relaxation time) and applied to inkjet process.   

Non-modal energy amplification in channel flows of viscoelastic fluids

Energy amplification in channel flows of Oldroyd-B fluids is studied from an input-output point of view by analyzing the responses of the velocity components to spatio-temporal body forces. These inputs into the governing linearized equations are assumed to be harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyze Newtonian fluid flows. It is found that the energy amplification increases with a decrease in viscosity ratio and increase in Reynolds number and elasticity number. In most of the cases, streamwise constant perturbations are most amplified and the location of maximum energy amplification shifts to higher spanwise wavenumbers with an increase in Reynolds number and elasticity number and decrease in viscosity ratio. For streamwise constant perturbations, an explicit Reynolds number scaling of energy amplification from different forcing to different velocity components is developed, showing the same $Re$-dependence as in Newtonian fluids. At low Reynolds numbers, the energy amplification decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.   

Fluid Dynamics and Rupture of Polymeric Solutions at Ultra-High Strain Rates

We create inertially-driven, nearly free, expanding rings to access rheology and flow phenomena of polymeric solutions at ultra-high strain rates. For a given fluid, with increasing initial velocity, three regimes are identified: expansion followed by elastic rebound, steady expansion, expansion interrupted by ruptures (cohesiveness failure). From expansion histories we deduce rheology (relaxation time and elasticity modulus) in the frame of the Oldroyd B model, and show that regime transitions can be captured consistently over a wide range of fluid constitutions by a single dimensionless group; that is the product of the Deborah number and an elasticity number---the elasticity modulus scaled by the initial flow kinetic energy. Moreover in this manner we find that: (a) the onset of rupture is determined by a specific value of tension (a critical rupture stress) which is characteristic on the solvent-polymer involved, and (b) the critical rupture stress scales in proportion to polymer concentration just as is the elasticity modulus. The method and results complement low strain-rate rheology, as in the well-known filament-thinning method, and is particularly well-suited for informing the micromechanics of rupture at high strain rates.   

Controllable adhesion using field-responsive fluids

Viscous Newtonian fluids confined in sufficiently small gaps can provide strong resistance to the separation of two parallel rigid surfaces, a phenomenon known as Stefan adhesion. However, the resistance to a shear load is considerably lower than for normal loads in such confined geometries. In principle, a field- responsive ``smart'' fluid, which exhibits a field-dependent microstructure with dramatically increased resistance to shear loading, can be used in place of a Newtonian fluid enabling externally-tunable adhesion. We report experimental results for both normal and shear loading of field-responsive, non- Newtonian fluids confined between rigid surfaces as the external magnetic field, the geometry of the adhesive contact pad, and the roughness of the adherent are varied. The peak adhesive force, the ``work of adhesion'' and the mode of failure are all controlled by the field-responsive nature of the magnetorheological fluid forming the adhesive layer.   

Session LU: Cyberfluids and Industrial Applications

An update on turbulence simulations at high core counts

Advances in computing power towards the Petascale via systems comprising $O(10^4)$ processor cores (and more) are creating great opportunities as well as substantial challenges for computational science, including direct numerical simulations of turbulence covering a wide range of scales in time and space. We present performance benchmarking data and discuss future optimization strategies for a code based on a highly scalable domain decomposition that allows up to $N^2$ cores on an $N^3$ periodic domain. Very favorable performance results have been achieved on new ``Track 2'' systems supported by NSF, up to $N=8192$ on 32768 cores and over a range of parameters including the choice of Cartesian processor-grid geometry for a given hardware configuration. Both strong scaling (increasing core count for fixed problem size) and weak scaling (core count varied in proportion to problem size) have been assessed in detail. The new algorithms are currently deployed in simulations at $4096^3$ resolution to achieve higher Reynolds number and to resolve the small scales better as suggested by recent literature. Plans for extension to more complex geometries and for sharing both data and codes with the wider Cyber-Fluid Dynamics community will be briefly addressed.   

Analysis of isotropic turbulence using a public database and the Web service model, and applications to study subgrid models

A public database system archiving a direct numerical simulation (DNS) data set of isotropic, forced turbulence is used for studying basic turbulence dynamics. The data set consists of the DNS output on 1024-cubed spatial points and 1024 time-samples spanning about one large-scale turn-over timescale. This complete space-time history of turbulence is accessible to users remotely through an interface that is based on the Web-services model (see http://turbulence.pha.jhu.edu). Users may write and execute analysis programs on their host computers, while the programs make subroutine-like calls that request desired parts of the data over the network. The architecture of the database is briefly explained, as are some of the new functions such as Lagrangian particle tracking and spatial box-filtering. These tools are used to evaluate and compare subgrid stresses and models.   

Open source PIV software applied to streaming, time-resolved PIV data

The data handling requirements for time resolved PIV data have increased substantially in recent years as the advent in high speed imaging and real time streaming. Therefore, there is a need for new hardware and software solutions for data storage and analysis. The presented solution is based on open source software (OSS) which has proven to be a successful means of development. This includes the PIV algorithms and flow analysis software. The solution, based on OSS known as ``URAPIV,'' originally was developed in Matlab and recently available in Python. The advantage of these scripting languages lies within their highly customizable platform; however, their routines cannot compete with commercially available software for computational speed. Thus, an effort has been undertaken to develop URAPIV-C++, a GUI based on the Qt 4 cross-platform open source library. This provides users with features commonly found in commercial packages and is comparable in processing speed to the commercial packages. The uniqueness of this package is in its complete handling of PIV experiments from the algorithms to post analysis under OSS license for large data sets. The package and its features are utilized in the recent STR-PIV system, which will be operable at the Advanced Facility for Avian Research at UWO. The wake flow behind an elongated body will be presented as a demonstration.   

The Process of Polymer-Turbulence Interactions leading to Polymer Drag Reduction

In a previous study we showed that the statistical properties of polymer drag reduction (DR) in the equilibrium state are found in homogeneous turbulent shear flow (HTSF) with the FENE-P model. We concluded that DR results fundamentally from an interaction among mean shear, turbulence, and polymer molecules. Here we develop insight into the mechanisms that suppress drag by analyzing the activation of polymer-turbulence interactions in HTSF and the transition to the equilibrium state as s function of shear Weissenberg number. We show that the initial state of polymer-turbulence interactions is different from equilibrium. Although both states follow from the suppression of smaller-scale turbulence strain-rate fluctuations by polymer stretching, the details depend on the ultimate level of DR. At early times and in the very low DR equilibrium state, DR is a direct consequence of the small-scale energy transfer from turbulence to polymer. At longer times and at higher drag reduction, DR results from the full elimination of the small scales and the restructuring of the remaining large-scale large vorticity by mean shear that statistically manifests as a suppression of slow pressure-strain energy transfer into vertical velocity. MDR is an asymptotic state in which the mean gradient interacts with polymer to maintain turbulence.   

Modeling of particle capture by mechanical means in automotive air filters

A model was developed to predict the removal of aerosol particles by automotive air filters. Filtration by direct interception, inertial impaction, and diffusion are correlated to dimensionless parameters. A Kuwabara flow field solution corrected for slip is applied to the flow around a single fiber. The contributions of the three filtration mechanisms are combined into a single-fiber efficiency, yielding overall filter performance. The accuracy of the new model is compared to simulated and experimental data of previous authors for two filter media. One medium has a mean fiber diameter of 0.65 $\mu $m and is examined for particle diameters of 0.01 to 1.0 $\mu $m with filter face velocities from 2 to 8 cm/s. A 2.7 $\mu $m diameter medium is considered for particle diameters of 0.1 to 1.0 $\mu $m with face velocities of 10 to 140 cm/s. For both media, the new model is a better predictor of filtration than our previous model. However, the results of the new model agreed more closely with experimental data for the larger-diameter medium for Stokes numbers less than 0.3, suggesting that direct interception and inertial impaction are predicted more accurately.   

Transient models of a displacement ventilation (DV) system and an underfloor air distribution (UFAD) system

Transient models of a displacement ventilation (DV) system and an underfloor air distribution (UFAD) system are examined theoretically and experimentally. We consider that a room heated by a single heat source represented as a buoyant plume and cooled with cooling diffusers. The cooling diffusers of DV system are assumed not to produce any appreciable mixing, while those of UFAD system are negatively buoyant jets which can mix warm air down from the upper part of the space. Conserving mass flux and buoyancy flux, the models determine the transient response of the temperatures in the lower occupied zone and the warm upper layer and the height of the interface between the layers. Non-dimensional transient models of DV and UFAD systems are derived by considering two competing time scales, the filling box time (Baines {\&} Turner 1968) which provides a measure for the establishment of the stratification and the replenishment time in which all the air in the enclosure is replaced by supply air. The models are examined by laboratory experiments using a salt-water analogy. The experiments show good agreement with the theoretical predictions for the initial transients in which the heat source and diffusers start simultaneously, and the time-varying heat or cooling loads simulating dynamic thermal responses in a real building.   

Application of a 3D Defocusing Particle Image Velocimetry System to a Virtual Impactor for Microscopic Aerosol Particles

A Defocusing Digital Particle Image Velocimetry (DDPIV) system is used to observe near-wall effects and flow instabilities within a virtual impactor section of an aerodynamic lens concentrator used to concentrate microscopic aerosol particles. The aerodynamic lens concentrator uses air as its main carrier gas which it draws from a small vacuum system. The DDPIV set up includes a 200mm close-up lens and a double pulsed laser used to backlight the field of view. The image volume is 1.76mmx1.32mmx1.83mm. A three-dimensional velocity field is extracted and the results are compared with preliminary CFD findings.   

Ocean Renewable Energy Research at U. New Hampshire

The University of New Hampshire (UNH) is strategically positioned to develop and evaluate wave and tidal energy extraction technologies, with much of the required test site infrastructure in place already. Laboratory facilities (wave/tow tanks, flumes, water tunnels) are used to test concept validation models (scale 1:25--100) and design models (scale 1:10--30). The UNH Open Ocean Aquaculture (OOA) site located 1.6 km south of the Isles of Shoals (10 km off shore) and the General Sullivan Bridge testing facility in the Great Bay Estuary are used to test process models (scale 1:3--15) and prototype/demonstration models (scale 1:1-- 4) of wave energy and tidal energy extraction devices, respectively. Both test sites are easily accessible and in close proximity of UNH, with {\em off-the-shelf} availability. The Great Bay Estuary system is one of the most energetic tidally driven estuaries on the East Coast of the U.S. The current at the General Sullivan bridge test facility reliably exceeds four knots over part of the tidal cycle. The OOA site is a ten year old, well established offshore test facility, and is continually serviced by a dedicated research vessel and operations/diving crew. In addition to an overview of the physical resources, results of recent field testing of half- and full-scale hydrokinetic turbines, and an analysis of recent acoustic Doppler surveys of the tidal estuary will be presented.   

Optimization of wafer-back pressure profile in chemical mechanical planarization

In chemical mechanical planarization (CMP), a rotating wafer is pressed facedown against a rotating pad, while a slurry is dragged into the pad--wafer interface to assist in planarizing the wafer surface. Due to stress concentration, the interfacial contact stress near the wafer edge generally is much higher than that near the wafer center, resulting in spatially nonuniform material removal rate and hence imperfect planarity of the wafer surface. Here, integrating theories of fluid film lubrication and two-dimensional contact mechanics, we calculate the interfacial contact stress and slurry pressure distributions. In particular, the possibility of using a multizone wafer-back pressure profile to improve the contact stress uniformity is examined, by studying a practical case. The numerical results indicate that using a two-zone wafer-back pressure profile with optimized zonal sizes and pressures can increase the ``usable'' wafer surface area by as much as 12\%. Using an optimized three- zone wafer-back pressure profile, however, does not much further increase the usable wafer surface area.   

Unsteady 3D flow simulations in cranial arterial tree

High resolution unsteady 3D flow simulations in major cranial arteries have been performed. Two cases were considered: 1) a healthy volunteer with a complete Circle of Willis (CoW); and 2) a patient with hydrocephalus and an incomplete CoW. Computation was performed on 3344 processors of the new half petaflop supercomputer in TACC. Two new numerical approaches were developed and implemented: 1) a new two-level domain decomposition method, which couples continuous and discontinuous Galerkin discretization of the computational domain; and 2) a new type of outflow boundary conditions, which imposes, in an accurate and computationally efficient manner, clinically measured flow rates. In the first simulation, a geometric model of 65 cranial arteries was reconstructed. Our simulation reveals a high degree of asymmetry in the flow at the left and right parts of the CoW and the presence of swirling flow in most of the CoW arteries. In the second simulation, one of the main findings was a high pressure drop at the right anterior communicating artery (PCA). Due to the incompleteness of the CoW and the pressure drop at the PCA, the right internal carotid artery supplies blood to most regions of the brain.   

Session LV: Chaos/Multifractality

Spatiotemporal chaos in the dynamics of buoyantly unstable chemical fronts

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for fronts traveling in the gravity field and for various values of the relevant parameters. These are here the Rayleigh numbers of the reactant $A$ and autocatalytic product $B$ as well as the ratio $D=D_B/D_A$ between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the fixed short wavelength dynamics of the diffusive instability can lead in some regimes to complex new dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we show the possibility of a transition between order and spatial disorder in this system. The analysis of the power spectrum further allows to identify similarities between the various spatial patterns while phase space representation is also discussed.   

Chaotic mixing in a curved pipe with periodic variations in curvature and torsion

The chaotic fluid mixing in a helix-like circular pipe with periodic variations in curvature and torsion caused by a steady viscous flow under an axial pressure gradient of relatively small Reynolds number is examined. An approximate equation obtained under the assumption of small and slowly-varying curvature and torsion is used to calculate the cross-sectional motion of fluid particles associated with their axial motion. We examine the dependences of mixing efficiency on a few geometrical parameters and on Reynolds number, and attempt to explain them by the variation in a characteristic ratio composed of curvature, torsion and Reynolds number.   

Topology of Chaotic Mixing Patterns

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a continuous mapping of a punctured surface. Having the rods undergo a topologically-complex motion guarantees a minimal amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods. See http://arxiv.org/abs/0804.2520 (Chaos, in press).   

Sky Dancer: a chaotic system

We present the experimental study of a collapsible tube conveying an ascending air flow. An extreme of the membrane tube is mounted on the air blower exit, while the other extreme is free. The flow velocity can be varied. For low speeds -- and tubes short enough -- the cylinder stands up (stable state). As the velocity is increased, the system presents sporadic turbulent fluctuations, when the tube bends and rises again. As the air speed is increased again, the intermittent events become more and more frequent. Films realized in front of the system permit to observe waves that propagate in the tube. We measure that these waves have a sonic speed, confirming previous results. Moreover, films taken from the top of the system allow a quantitative characterization of the transition to chaos. By processing the images, we can reduce the evolution of the system to two states: stable (when it is raised) and chaotic (when the tube fluctuates). The histograms of unstable / stable states are coherent with an intermittent transition in the theory of chaos.   

Multifractal Analysis of Vortex Pair Formation of Modified Taylor-Couette Flow in Laminar and Turbulent Regimes

For sufficiently large effective Reynolds Numbers the formation of Taylor Vortex Pairs in Modified Taylor-Couette flow with hourglass geometry becomes irregular in time. At higher effective Reynolds Numbers the flow becomes turbulent, but Taylor Vortices may still be discerned. Again, for sufficiently high effective Reynolds Numbers, the formation of these vortex pairs becomes chaotic. Previously we have demonstrated that each process may be characterized as low dimensional chaos.\footnote{A. Kowalski, T. Olsen, \& R. Wiener, Bull. Am. Phys. Soc. \textbf{50-9}, P1.00030 (2006).} We now present a multifractal analysis\footnote{J. A. Glazier \& A. Libchaber, IEEE Trans. On Circuits and Systems \textbf{35-7}, 790 (1988).}$^,$\footnote{T. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, \& B. I. Shraiman, Phys. Rev. A \textbf{33}, 1141 (1986).} of these processes.   

Topological chaos in wide lid-driven channels

Rapid fluid mixing can be produced in laminar flows through a high-aspect-ratio microchannel by means such as pressure-driven flow with staggered surface groove patterns or electro-osmotic flow with potential differences between the upper and lower boundaries. Under certain conditions, passive fluid particles or groups of particles can act as ``rods'' that stir the surrounding fluid and produce exponential stretching. The occurrence of ``topological chaos'' guarantees rapid mixing in these flows, and the Thurston-Nielsen theorem predicts a quantitative lower bound on complexity in the dynamics of the flow. We will present an exact solution for two-dimensional Stokes flow in a lid-driven cavity with periodic side wall boundary conditions and extend this model to approximate three-dimensional channel flow. We will examine the occurrence of topological chaos in these flows and discuss the mixing efficiency.   

Chaotic advection in pulsed source-sink systems

Pulsed operation of a source and a sink is a classic approach to generating chaotic advection in the unbounded plane. This approach provides motivation for mixing laminar flows in high-aspect-ratio volumes using an arrangement of sources and sinks.~ In bounded systems the sources and sinks must operate in pairs in order to conserve volume.~ When the sources and sinks are arranged on the boundary of a circular domain, particle motions are given explicitly by a discrete mapping. This mapping is used to explore the optimal operating parameters for producing chaos with three different source-sink configurations in a circular domain.   

Topological chaos in flows on surfaces of arbitrary genus

The emerging field of topological fluid kinematics is concerned with design and analysis of effective fluid mixers based on the topology of the motion of stirring apparatus and other periodic flow structures. Knowing even a small amount of flow topology often permits very powerful diagnoses, such as proving existence of chaotic dynamics and a lower bound on mixing measures based on material stretching. In this paper we present a canonical method for examining flows on surfaces of arbitrary genus given the flow topology encoded as a braid. The method may be used to study fluid mixing driven by an arbitrary number of stirrers in either bounded or spatially periodic fluid domains. Additionally, and unlike previous techniques, the current work may also be applied to flows on manifolds of higher genus.   

Chaotic mixing and superdiffusion in a two-dimensional array of vortices

We present experimental and numerical studies of mixing and long-range transport in an array of vortices forced by a magnetohydrodynamic technique. A current passing horizontally through a thin electrolytic solution interacts with a magnetic field produced by an array of magnets below the fluid. If the current is parallel to one of the primary directions of the magnet array, a square array of vortices is produced. If the current is tilted with respect to the magnet array, however, wavy channels form diagonally through the vortex pattern, allowing tracers in the flow to travel long distances in a short period of time. The addition of a time-dependent current results in a combination of chaotic and ordered vortex/jet regions that produces Levy flights and superdiffusive transport. If an AC current is applied in both cardinal directions, the resulting chaotic mixing is typically barrier-free.   

Unmixed islands in quasi-periodically-driven flows

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a quasi-periodically forced fluid flow. The Hamiltonian describing this system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincar\'{e} sections of the flow. The coherent structures (cross-sections of nested 2-tori) are found to each have a fractal dimension of two, in each Poincar\'{e} cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.   

Session LW: Mini-Symposium: High Rayleigh Number Convection: Is there an ultimate regime?

Nusselt and Reynolds numbers for turbulent convection at very large Rayleigh numbers

This talk will present a brief review of available Nusselt- and Reynolds-number measurements relevant to the issue of the transition to the ``ultimate'' regime of turbulent Rayleigh-Benard convection discussed by Kraichnan. It will then examine the expected signature of such a transition in the dependence of the Nusselt number on the Rayleigh and Prandtl numbers. Finally it will discuss future prospects for new measurements at very large Rayleigh numbers that will be potentially relevant to the transition.   

Comparative study of the hot and cold thermal boundary layers in turbulent Rayleigh-Benard convection

We report a comprehensive series of measurements of the mean temperature profiles in turbulent Rayleigh-Benard convection of air in a cylindrical cell with aspect ratio one and Rayleigh numbers in the range 10$^{11}$ to 10$^{12}$. The measurements differ from those reported in the paper du Puits et al [J. Fluid Mech., vol. 572 (2007), pp. 231-254] in that the profiles are taken simultaneously at the heating and the cooling plates and that we can directly measure the local heat flux at the heating plate. In the present communication we will discuss the results of these measurements and compare them to previous ones as well as to recent predictions about the asymptotic shape of the mean temperature profiles derived by Hoelling and Herwig [Int. J. Heat Mass Transf., vol. 49 (2006) pp. 1129-1136]. In collaboration with Christian Resagk and Ronald du Puits, Ilmenau University of Technology.   

Temperature Oscillations and Flow Dynamics in Turbulent Thermal Convection

We report an experimental study of three-dimensional structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-B\'{e}nard (RB) convection cell of aspect ratio one. It is found that the hot and cold thermal plumes are not emitted periodically nor alternatively, but continuously and randomly, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting oscillation near the top and bottom plates and the off-center oscillation in the bulk flow field. Evidence will also be presented to show that the off-center oscillation in the bulk flow field is a manifestation of the twisting motion of fluid near the top and bottom plates. In collaboration with Heng-Dong Xi, Quan Zhou, and Sheng-Qi Zhou, The Chinese University of Hong Kong.   

The Heat Transport Law In Thermal Convection

This talk will survey the outstanding elements of the heat transport law in thermal convection. It will particularly focus on the author's work on this problem carried out in collaboration with a number of his colleagues and students. From a combination of experimental and numerical studies, which have pushed the limits of Rayleigh (Ra) and Prandtl (Pr) numbers, we deduce the dependence of the Nusselt number (Nu) on Ra and Pr. These studies include the consideration of non-Boussinesq effects, imperfect boundary conditions, the role of aspect ratio, and so forth. Our conclusion is that Nu is proportional to the one-third power of Ra for large Ra, and that the so-called asymptotic form, which stipulates a 1/2 power instead of the 1/3, does not arise in thermal convection in the presence of solid boundaries. Some remarks will be made also about the dependence of Nu on Pr.   

Numerical simulations of thermal convection at high Prandtl numbers

Direct numerical simulations of thermal convection are conducted for a cylindrical cell of aspect ratio $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $. The Prandtl number (Pr) varies from 10$^{0}$ to 10$^{4}$ and the Rayleigh numbers (Ra) are moderate (10$^{5} \quad <$ Ra $<$ 10$^{9})$. This study is motivated by the fact that the role of the Prandtl number in convective heat transport is not yet fully understood. The three-dimensional behaviors of the temperature and velocity fields, of the viscous and thermal dissipation fields, and of the diffusive and convective heat fluxes are explored. In the ranges of Pr and Ra considered, we find steady, periodic and chaotic regimes, and large-scale structures which are more complex than the single recirculation cell filling the whole volume. Multiple flow structures are found to be associated with a given set of conditions. The multiple solutions seem to be more probable at higher Pr numbers and could explain the scatter in some data trends. In collaboration with Katepalli Raju Sreenivasan, The Abdus Salam International Centre for Theoretical Physics - Trieste, and Roberto Verzicco, DIM, Universit\`a degli Studi di Roma Tor Vergata - Roma.   

Session LZ: Poster Session (15:15 - 17:00)

Design, construction and characterization of a solar thermoacoustic engine

We designed, constructed and characterized a thermoacoustic engine that operates with solar radiation concentrated by a Fresnel's lens. The resonator is a Pyrex tube closed in one of its ends and opened in the other one. The stack is built of a ceramic piece with parallel channels. The Fresnel's lens concentrates the direct solar radiation on the end of the stack near to the closed end of the resonator. A structure supports the elements of the engine and allows following the direct solar radiation in a manual form. The acoustic pressure amplitude of the generated stationary wave was measured with a microphone located 1 cm away from the opened end, but it was impossible to measure it in the closed end since the concentrated solar radiation goes through this end, and the placement of any microphone would obstruct its passage. Therefore we made an engine warmed by an electrical resistance in which it is possible to place a microphone in both ends of the resonator. Using the electric engine we reproduced the wave generated by the solar engine to estimate the acoustic pressure amplitude in its closed end.   

Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow

Embedded vortices in wall-bounded flow over a flat plate, generated by a passive rectangular vane-type vortex generator with variable device angle $\beta$ to the incoming flow in a low- Reynolds number flow ($U_{\infty} = 1.0\, ms^{-1}$), have been studied using Stereoscopic PIV in the respect of helical symmetry. The vortices possess helical symmetry, allowing the flow to be described in a simple fashion. A model describing the flow has been utilized, showing strong concurrence with the measurements. Through the swirl parameter it was possible to predict the helical pitch. The pitch, vortex core size, circulation and the advection velocity of the vortex all vary linearly with $\beta$. One can thereby determine the axial velocity induced by the helical vortex as well as the swirl for a given $\beta$. This also simplifies theoretical studies, e.g. to understand and predict the stability of the vortex and to model the flow numerically.   

Minimum Drag Shape of a Hemi-ellipsoid Exposed to Shear Flow and Its Possible Relation to Deformation of Arterial Endothelial Cell

As a model problem for an endothelial cell subject to blood flow, we consider a hemi-ellipsoid attached to a wall in the imposed shear flow. The minimum drag shape is obtained under the condition that the volume is kept constant. The aspect ratio of major axis to minor axis of the minimum drag shape turns out to be close to those of the equilibrium shapes of endothelial cells under steady blood flow. This fact suggests that there might be a possible connection between the objective function of drag minimization and the feedback mechanism for shape adjustment of an endothelial cell. From the fluid mechanics point of view, this mechanism can be considered as that the endothelial cell adjusts its shape in a way to minimize the drag force exerted by the shear flow. The analytical solution to the model problem is not available. So, the problem is solved numerically to compute the drag force exerted on the hemi-ellipsoid. However, an analytical solution is available for a closely related problem, which is the problem of a fixed ellipsoid in a shear flow. When the upper half domain is considered, the analytical solution satisfies everything of the original problem except for the velocity y-component at the flat surface. The analytical solution is Jeffery's classic result on the motion of an ellipsoidal particle in a viscous fluid [Proc. Roy. Soc. A (1922)].   

The influences of curvature and torsions on flows in a helical bifurcated stent-graft

A bifurcated stent-graft signifies an improvement in surgical technique for treatment of a lesion in the branched blood vessel. However, there still remains a high failure rate regarding bifurcated stent-graft due to the occurrence of thrombosis or re-stenosis. The objectives of this study are to understand the effect of torsion in helical bifurcated geometries, to explain how the mixing of flows there may be advantageous to the prevention of the occurrence of thrombosis, and to keep the patency of stent-graft in the aspect of hemodynamics. For clinical applications, flows in a helical bifurcated stent-graft are simulated three-dimensionally using an incompressible Navier-Stokes solver. In this study, the hemodynamics is investigated in terms of mechanical factors, i.e., velocity profiles, vortex patterns and wall shear stress distributions.   

Migration of connexin in the membranes of living cells

Movement of connexins within cell lipid bilayers remains somewhat mysterious. In studying their movement, researchers hoped to shed more light on the mechanisms by which they are influenced. We examined this problem by observing the behavior of the connexins directly. Cancerous human liver cells were cultured and their membrane connexins labeled with green fluorescent protein through transvection. The connexins were then filmed by high speed camera and carefully analyzed. The study served to fine-tune the model used in simulations of connexin migration, enabling further study of connexins and their transmembrane environment.   

Nonlinear effects in the dynamics of viscous vesicles in linear flows

Vesicles in a simple shear flow deform into prolate ellipsoids and exhibit at least three (experimentally confirmed) types of behavior: tank-treading (also observed for drops), tumbling and breathing (new features that are unique for vesicles). This non- trivial dynamics originates from the distinctive mechanical properties of the lipid bilayer membrane: the molecularly thin membrane is a highly-flexible incompressible fluid sheet. Several groups have studied vesicle behavior in steady shear flow. The phase diagram suggests that when subjected to linear flow with some variable parameter, vesicle transition between different states can show hysteresis. We examine dynamics of vesicles subjected to time-varying flows: oscillatory shear and linear flows with variable rotational component. Floquet analysis is conducted to investigate the vesicle dynamics and conditions for chaotic shape and flow dynamics are established.   

Taylor-Couette Flow with Hourglass Geometry of Varying Lengths Simulated by Reaction-Diffusion

Previously, we have observed chaotic formation of Taylor-Vortex pairs in Modified Taylor- Couette Flow with Hourglass Geometry.\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).} In the experiment, the chaotic formation in a shorter system has been restricted to a narrow band about the waist of the hourglass. Such behavior has been modeled by The Reaction-Diffusion equation,\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} which has been previously studied, by Riecke and Paap. Their calculation suggested that quadrupling length of the system would lead to spatial chaos in the vortex formation. We present a careful recreation of this result and consider an intermediate length. We demonstrate that doubling the length should be sufficient to observe spatially chaotic behavior.   

Control of the Damped, Driven Pendulum, in both Numerical Models and Physical Apparatus to develop algorithms appropriate to the control chaotic formation of Taylor Vortex Pairs in Modified Taylor-Couette Flow

Chaos has been observed in the formation of Taylor Vortex pairs in Modified Taylor Couette flow with hourglass geometry.\footnote{Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).} Control of chaos has been demonstrated in this system employing the RPF algorithm.\footnote{Rollins \textit{et al}, Phys. Rev. E \textbf{47}, R780 (1993).}$^,$\footnote{Wiener \textit{et al}, Phys. Rev. Lett. \textbf{83}, 2340 (1999).} Seeking alternative algorithms, we are implementing the OGY\footnote{E. Ott, C. Grebogi, \& J. A. Yorke, Phys. Rev. Lett. \textbf{64}, 1196 (1990).} algorithm in a numerical model\footnote{G. L. Baker, Am. J. Phys. \textbf{63}, 832 (1995).} of a damped driven mechanical pendulum and a physical apparatus.\footnote{J. A. Blackburn \textit{et al}, Rev. Sci. Instr. \textbf{60}, 422 (1989).} We report on both and future plans for the Modified Taylor-Couette system.   

Theoretical Studies of Transport within Single Walled Carbon Nanotubes

Carbon nanotubes have exciting electrical and mechanical properties that seem attractive for ionic and non-ionic transport. However, some fundamental questions about this transport are still not completely understood. One of these questions is how the ion transported through the nanotube is affected by the force and electric fields of the nanotube due to its size and charge. For this investigation to be done, a theoretical structure for a (5,5) single walled carbon nanotube (SWCN) is created by optimizing the geometry of a (5,5) SWCN using semi-empirical PM3 methods. With that optimized structure, computer simulations are performed based on Molecular and Brownian Dynamics techniques to analyze the diffusion through the SWCN. We calculate diffusion coefficients, mean square displacement as well as concentration profiles for both ionic and non-ionic particles moving through them.   

Migration of Connexin in the Membranes of Living Cells: Computational Method

The membranes of living cells are semi-permeable layers that contain phospholipids and numerous proteins. Connexin, specifically, is a gap-junction protein found in the membrane that is imperative in the communication between cells. We utilized a lattice Boltzmann simulation to model the motion of connexin within a cellular membrane. The phospholipids are considered a uniform fluid in the simulation. The model membrane contains solid obstacles that impede the movement of connexin, thus causing the protein to become trapped in domains for various periods of time. The results from the computational model have been used to quantitatively match the results of an experiment involving cells with connexin labeled by green fluorescence protein. We also use the simulation to investigate different mechanisms by which connexin migrates to the point of contact between cells.   

Heat Convection in a Vertical Channel

The Rayleigh-Benard flow, heat convection between two horizontal plates at different temperatures, has been the most studied system of thermal convection. Recent controversies stressed the interest of a better knowledge of the bulk flow. However,~ in this situation, the heat transfer is mainly controlled by the neighborhood of the plates. Therefore, we had to build a vertical long channel in which the flow forgets the plates. In this configuration, the flow is, either globally ascending in the left part, and descending in the right one, or the opposite. The paper focuses in a first part on the study of these flow-reversals thanks to correlation functions and particle image velocimetry. In a second part, the paper gives an interpretation of results in terms of velocity of plumes.   

Laboratory measurements of energy and temperature dissipation rates in Rayleigh-Bernard convective flow with Ra= O(10$^8$) to O(10$^9$)

The measurements were carried out in a Rayleigh-Bernard convective cell with dimensions 0.3 m x 0.3 m x 0.3 m. We have experimentally obtained time series of temperature collocated with velocity fields from a 2D PIV system.~The length of the time series spans a few large eddy turnover times, allowing the capture of energy and temperature fluctuations. We have used PIV interrogation windows smaller than the Kolmogorov scale, permitting calculation of the energy dissipation rates.~The energy dissipation rates were calculated using methodology following (Fincham et al. 1996). The temperature variance dissipation rates were calculated using collocated time series of microscale velocity and temperature fluctuations. The obtained temperature variance dissipation rates were compared to the measurements of this quantity performed using optical techniques following (Bogucki et al. 2007). The structure of the large scale velocity flow reflects the observations of (Xia et al. 2003), while we note some departure of the PDF of temperature and velocity from a Gaussian distribution.   

Bifurcations in convection of incompressible fluid in a rotated square cylinder

The 2D convection of air in a long horizontal square cylinder two opposite side walls of which are thermally insulated and the other two are maintained at constant but different temperatures has been considered. The cavity is gradually rotated about its horizontal axis. It is found that a multitude of stationary bifurcating solution exist depending on the inclination angle and the Rayleigh number. Normally and abnormally rotating solutions are defined and distinguished and the bifurcation curve is computed.   

Capillary forces during liquid nanodispensing

Liquid nanodispensing (NADIS) is a recently developed method to deposit and manipulate small volumes of liquids (down to 100 zeptoliter) on a surface [1]. This atomic force microscope (AFM)-based method uses a nanochannel milled by focused ion beam (FIB) at the apex of a hollow AFM tip to transfer liquid from a reservoir located on the cantilever, to the surface. The smallest droplets (70 nm in diameter) contain, for standard dilutions, only few molecules opening the way to single molecule deposition. We present here a study of the capillary force exerted on the tip during the deposition. Using the ``surface evolver'' software, we simulated the force curves measured by AFM, which is the only available data during deposition. The good agreement between experimental and calculated curves gives important information on the liquid transfer mechanism and provides a real-time control of the deposition during the process [2]. \\[0pt] [1] A.Fang, E. Dujardin, T.Ondarcuhu, NanoLett. 6 (2006) 2368. \\[0pt] [2] T.Ondarcuhu et al, Eur. Phys. J. ST. (2008) in press.   

Nonlinear hydrodynamic phenomena in Stokes flow

The inertial term in the Navier--Stokes equations gives rise to numerous nonlinear phenomena, such as flow instabilities, formation of complex convective patterns, and turbulence. In our presentation we will discuss nonlinear behavior of a fluid under Stokes flow conditions, i.e., with no inertial forces. The fluid-dynamics equations are thus linear---the nonlinearity of the system stems entirely from the boundary conditions. We will consider (a) the dynamics of a highly viscous drop in 2D linear flows with rotation and (b) the motion of regular particle arrays in Poiseuille flow in a parallel-wall channel. We show that the drop response to quasistatic vorticity change is hysteretic, and at higher frequencies of the external forcing, the system undergoes a cascade of period-doubling bifurcations leading to chaos. We also demonstrate that the evolution of regular particle arrays in parallel-wall channels leads to emergence of complex patters that include separation of double rows of particles from the main body of the array, coexistence of ordered and disordered regions, rearrangements of regular particle lattice along dislocation lines, and fingering instabilities.   

Evolution of precursor film in front of the moving contact line of spreading drop

For wetting fluids, a microscopic film, which is known as the precursor film, exists at the front of the moving contact line. The structure of this thin film has been studied theoretically, but previous experimental investigations were limited by the resolution of the measurement system (lateral or vertical) required to capture the complete scope of this feature. We studied the evolution of the profile of a spreading droplet near the moving contact line using a total internal reflection fluorescence microscope (TIR-FM). The features of the macroscopic drop (spherical cap), wedge region, and precursor film were investigated within a single experiment. This was made possible by the lateral resolution and dynamic range of our technique. The dynamic characteristics of the precursor films have a good agreement with the available theoretical results.   

Growth and shape of bubbles in viscous liquids and confined geometries

In this work we have considered the problem of the growth and detachment of bubbles in a viscous liquid in finite reservoirs where axisymmetrical walls were located near the gas injection orifice. We studied numerically and experimentally how the coaxial pipe and inverted-cone walls affect the shape, final volume and coalescence of bubbles under conditions of constant gas flow rate, Q. The numerical solution of the Stokes equations and the free surface were determined as a function of a capillary number and Bond number in the absence of inertial effects. Detailed experimental visualizations are presented that display the sequences of growth and detachment computed numerically.   

Field-induced motion of ferrofluid droplets through immiscible viscous media

The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. Results for a range of magnetic Laplace number and magnetic Bond number are given. The time taken by a droplet to travel through a viscous medium and the deformations in the drop are investigated and compared with experimental studies.   

Interaction of a contact line with nanometric steps

In order to study the interaction of a contact line with nanometric steps, we investigated the dewetting of polystyrene films on terraced surfaces such as alumina or graphite (T. Ondarcuhu, A. Piednoir NanoLett 5 (2005) 1744-1750). We observed that, for steps heights larger than a critical value, the hole is asymmetric: the contact line is blocked by downwards steps whereas it passes through upwards steps with no interaction. This behavior is explained by simple macroscopic considerations based on the equilibrium contact angle. For steps smaller than this critical value, the contact line is insensitive to the steps: the hole grows symmetrically as on a homogeneous surface. Statistics with various polystyrene over a large number of steps on alumina showed that the critical step height is about 3 times the radius of gyration of the polymer. This indicates that a simple ``macroscopic'' description remains valid down to dimensions of the order of the diameter of one single molecular chain. This result has also important implication for the study of contact angle hysteresis.   

The thermogravitational technique at high pressures

Thermogravitational columns have been used successfully for over a decade to experimentally determine the thermal diffusion coefficients of binary and ternary mixtures at atmospheric pressure. A homogeneous mixture is placed in a vertical annulus. Species separation occurs due to side heating and thermal diffusion. Combined with buoyancy vertical concentration gradients are induced, measured, and the Soret coefficients deduced. In this work we extend this technique to measurements at the high pressures encountered in oil fields. A detailed description of the high pressure thermogravitational installation is presented. We first validate the new construction by conducting experiments with binary mixtures at atmospheric pressure and comparing our results with those in the literature. Dependence of the thermal diffusion coefficients of various binary mixtures of hydrocarbons and liquids on pressure is given.   

Simultaneous Reference- and Pressure-Image Acquisitions for Unsteady Pressure-Sensitive Paint Measurement

Simultaneous reference- and pressure-image acquisitions using two-color unsteady pressure-sensitive paint (PSP) and a stereo adaptor are presented. Unsteady PSP gives two-color luminescence, which is related to reference- and pressure-images, respectively. Two band-pass filters matching with reference- and pressure-luminescence, respectively, are mounted in front of a stereo adaptor to capture only reference- and pressure-images. The adaptor is connected to a fast frame rate CCD camera that can acquire continuous unsteady pressure field. Our acquisition system has an advantage for unsteady PSP measurements that fluctuate and/or vary reference image in time. The validity of this system is discussed. A demonstration of the present system in unsteady pressure field with model fluctuation is included in the final version.   

Experimental spectroscopy for the high-school Physics curriculum

The present work explores the feasibility of including spectroscopic experiments in high-school physics curricula. Two experimental optics ``modules'' were constructed for this purpose: (a) a simple CCD detector, in combination with appropriate filters, was used for the measurement of solar spectra and the determination of the sun's surface temperature; (b) the same detector was used, in combination with a transmissive diffraction grating and some miniature optics, to form a spectrophotometer that can be used for the determination of spectra with high resolution. Both modules were designed and constructed with portability and low cost in mind, and their objective is to introduce experimental spectroscopy to high school students in an intriguing, educational and phase-appropriate manner without sacrificing scientific rigor. A large variety of experiments may be designed around the basic devices that were built during this work, and a number of possible examples will be presented, from research on plant phototropism to human color cognition.   

Longitudinal cross sectional mixing images of the pipe flow with periodical branching flow injections

Effect of periodical injection of branching flows on the mixing in a pipe flow is experimentally investigated. Glycerin is used as a working fluid. The glycerin flows in a steady state condition in the main flow pipe while the branching flow is injected periodically from three pipes equipped normal to the main flow pipe. The longitudinal cross sectional image of the mixing of main flow and branching flows is visualized by LIF method, inserting the Rodamine B in the first branching flow. When only one branching flow is periodically injected, the fluid injected from the side flow pipe is stretched and folded by the parabolic laminar flow velocity profile and then the length of the boundary increases linearly. When branching flow is injected from multiple side flow pipe, the mixing pattern becomes more complicated. As a result, the length of the boundary increases more rapidly compared to the linear increase. The results suggest that the multiple branching flow injection enhances the mixing although no element is inserted in the pipe.   

Streaky 3D Structures in the Boundary Layer

It has been recently shown [Choi, Nature, April 06 - Cossu, PRL, February 06] that 3D streaky structures in the boundary layer can remain laminar longer than the 2D Blasius flow. The aim of this investigation is to study the possibility of promoting these 3D streaky structures via surface roughness, computing them and evaluating the resulting stabilization using the Reduced Navier Stokes equations (RNS). The RNS are derived from Navier-Stokes making use of the fact that two very different scales are present: one slow (streamwise direction) and two short (spanwise and wall-normal direction). The RNS allows us to perform these 3D computations in a standard PC, without using CPU costly DNS simulations.   

Collapsing Mechanism of Toroidal droplets

Water drops in oil phase are always spherical in order to minimize interfacial energy. This is why other drop shapes are rarely seen. This report show that we are able to generate millimeter size drops which are topologically different from the sphere, namely a torus. The torus can be made by rotating an outer oil phase fast enough while pumping water through an oil submerging capillary tip. For large values of the capillary number of the outer fluid we can create a circular jet which becomes a full circle to make a torus drop. The fatness of the torus can be control through the volume of infused water and the location of the capillary tip from the center of rotation. The toroidal droplets always evolve into a spherical shape. The mechanism of this process is very interesting. So far we have classified two types of behaviors. For a skinny torii, break-up occurs followed by a slow evolution towards the spherical shape. For fat torii, however, there is no break-up. In this case, the torus gets fatter as a whole ultimately collapsing into a spherical drop. We have quantified the dimensionless growth rate for these two situations and compared our results with predictions based on the Rayleigh-Plateau instability for the experimental viscosity ration; the comparison suggests that more ingredients must be incorporated to explain our data.   

Richtmyer-Meshkov Instability in Thin Fluid Layers: Turbulent Mixing, Mach Number and Reshock Effects

A thin air-SF6-air gas curtain is impulsively accelerated by planar shock waves of varying strength (Mach 1.2-1.5) and investigated experimentally using simultaneous concentration field visualization and particle image velocimetry measurements. A novel nozzle design is used to create highly repeatable and flexible initial conditions that allow for isolation of effects on the flow structure due to Mach number and initial modal composition. The effective position of the end wall is also varied to re-shock the evolving structure, accelerating the transition of the flow to a turbulent regime. Turbulence statistics are compared between a single mode varicose curtain, and a multi-mode curtain. These true-ensemble averaged statistics are the first such measurements in variable density turbulent flows in thin fluid layers, and can be used for code validation.   

Experimental Investigation of the Stability of a Stratified Fluid Flow Involving a Horizontal Gradient of Density

A vertically moving boundary in stratified fluid can create and maintain a horizontal density gradient, with greater density fluid adjacent to the moving boundary. We have designed an experiment to study the hydrodynamics of this configuration, whereby the moving boundary consists of a fishing line towed vertically through a stably stratified fluid. A shear boundary layer is observed to develop in the fluid resulting in a horizontal density gradient. We measure the size of the shear layer as a function of the speed at which the line is towed. The hydrodynamic instability of this system manifests itself as an apparent jump in this plot. Consequently, we are able to obtain a critical Reynolds number for the stability of this system. We also compare the layer size-to-speed observations with those obtained from an exact mathematical solution which approximates the geometry of the problem in the axial-symmetric case.   

Visualization study of the vapor bubble dynamics in the liquid nitrogen flow inside a small tube

The vapor bubble nucleation, growing up and detachment in diabatic two-phase flow of liquid nitrogen in a vertically upward tube of 1.33 mm in diameter is experimentally investigated by employing high-speed visualization technique. It can be found from the experiments that the vapor bubble diameter increases linearly with the elapse of the time. The tube wall has the significant effect on the vapor growing up process. In the initial stage, the vapor bubble expands in both radial and axial directions; while the growing up of vapor bubble in radial direction is impeded and the growing up along the axial direction speeds up when the diameter of the vapor bubble equals the tube diameter. The flow reversal will appear when the expanding velocity of the vapor bubble is larger than that of the flow velocity. The nucleation sites display different characteristics in that the detachment of vapor bubbles from the nucleation sites downstream is more frequent and the diameter of the vapor bubble is smaller.   

Analysis of the plane Poiseuille flow of a wormlike micellar solution with shear banding

In this work a detailed study of the plane Poiseuille flow of a shear banding wormlike micellar aqueous solution is presented. The experiments were carried out at 27.5 \r{ }C under controlled pressure using a transparent flow cell, where simultaneous measurements of polarimetry, pressure drop and flow rate were performed in order to asses the flow stability. Particle image velocimetry was also used to analyze the flow kinematics upstream of the contraction. Five different regimes were observed in the flow curve, as well as the development and growth of shear bands right before the spurt. After the transition to the high shear branch, the flow became unstable and was composed by asymmetric shear bands of structured and isotropic fluid, which oscillated with respect to the zero-shear plane. Symmetric lip vortices were observed to grow and suddenly decrease under unstable flow conditions upstream of the contraction. The shear bands oscillated in the same way as upstream vortices with a frequency that increased along with flow rate. The oscillating flow upstream of the contraction arise from changes in the vortices size and produced jets or spurts of highly oriented material followed by recoiling of the micellar solution.   

Experimental Study of Heavy Oil Displacement by Hot Water in Porous Media

The injection of one fluid to displace another in a porous medium is the basis of many industrial processes such as Enhanced Oil Recovery (EOR). EOR applications are encouraged by high oil prices and growing oil demand. Therefore, performance prediction of EOR processes is of great importance to their success. Core flooding experiments are well known practices in the petroleum industry that provide economical means of determining the responses of reservoir rock and fluids to the driving mechanism responsible for production. Lab experiments provide both insight into the behavior of fluid displacements and data with which to test and calibrate numerical simulators. In this study, laboratory experiments were conducted in order to test the effectiveness of hot water injection to displace heavy oil from a given porous medium. The objective was to find the optimum design parameters in terms of injection temperature and hot water slug size that will yield the best performance. Analysis of these experiments has revealed the functional relationships between the scaling groups describing the displacement and the oil recovery obtained from such displacement. Results obtained from several design configurations are presented. These relationships can be used as a tool for the design of hot water injection to recover heavy oil. They also provide conditions under which a given design may yield better recovery performance.   

Capillary Rise and Flow of Complex Liquids in Nanopores

We present measurements on the capillary rise (spontaneous imbibition) and pressure driven flow (forced imbibition) of liquids into silica monoliths (namely porous Vycor) permeated by tortuous pores with radii of 4.4nm (V10) and 3nm (V5) resp. The flow properties are studied as a function of the complexity of the building blocks of the liquids (water, n-alkanes and liquid crystals), of shear rate and temperature in the case of the liquid crystal.   

Visualization of Velocity Profile on Separately Applied Hydrophobic and Hydrophilic Surfaces

A chemical flow control method using functional chemical is discussed. In our previous tests, we showed that separately applied hydrophobic and hydrophilic coatings with six different patterns on an ogive shape model could control the dropping speed by maximum 22 percent at the Reynolds number of 1.0E6. In the present study, we focused on the velocity profile on the coated surface. We use Fusso51 from Yukawa as hydrophobic coating and WaterX from Nishikinodo as a hydrophilic coating. Contact angles of these coatings are 130 degree and 5 degree, respectively, on anodized aluminum surfaces. These coatings are separately applied on a 2D profile. A hydrogen bubble technique is used to visualize its velocity profile related to the coatings.   

Wall free energy based polynomial boundary conditions for non-ideal gases lattice boltzmann simulation

Intermolecular forces between solid and liquid can be represented by the inclusion of the wall free energy in the expression of the total free energy for the bulk phases. We derived and investigated three types of polynomial (linear, quadratic, and cubic) wall free energy boundary conditions for the non-ideal gas lattice Boltzmann equation (LBE) method. Both static and dynamic drops on solid surfaces are examined. All the proposed boundary conditions are able to predict the equilibrium states very well in the moderate contact angle range by incorporating appropriate potential form of the intermolecular forces and the bounce-back rule that guarantees mass conservation for both static and dynamic cases. Simulations with different boundary conditions are carried out and the results are compared concerning the accuracy as well as the applicability of different boundary conditions. Numerical results show that the cubic boundary condition has the fastest spreading rate among the three types of the boundary conditions, while, due to the neglect of vapor-solid intermolecular forces and the highly elevated liquid density at the hydrophillic surface, the quadratic boundary condition demonstrates the slowest spreading rate.